Re: [sage-edu] Extreme graphing
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Dan Drake
Feb 28, 2013, 5:21:06 PM2/28/13
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On Thu, 28 Feb 2013 at 11:56AM -0800, David Smith wrote:
> I've been experimenting (in an interact) with graphing x^m/e^x for large
> values of m, in order to demonstrate that exp grows faster than any power
> function. This works fine up to m=15, but at 16 (and any higher value) I
> get a long list of errors ending with
>
> ParseFatalException: Expected end of math '$'
> $\verb|1e+12|$ (at char 0), (line:1, col:1)
>
> Wolfram Alpha is perfectly happy to graph this function up to m=125, and after that, it fails only in lopping off the top of the graph because the y-coordinates are too big.
> Is there some reason why Sage can't handle this?
For me, Sage works fine up to x^115. There it starts to complain that it
can't evaluate the function (x^115/e^x) at all points. That seems very
strange to me, although maybe it's running up against the
maximum size that floats can do -- but the plot looks fine, so maybe
not?
Dan
--
--- Dan Drake
----- http://math.pugetsound.edu/~ddrake
-------
> I've been experimenting (in an interact) with graphing x^m/e^x for large
> values of m, in order to demonstrate that exp grows faster than any power
> function. This works fine up to m=15, but at 16 (and any higher value) I
> get a long list of errors ending with
>
> ParseFatalException: Expected end of math '$'
> $\verb|1e+12|$ (at char 0), (line:1, col:1)
>
> Wolfram Alpha is perfectly happy to graph this function up to m=125, and after that, it fails only in lopping off the top of the graph because the y-coordinates are too big.
> Is there some reason why Sage can't handle this?
For me, Sage works fine up to x^115. There it starts to complain that it
can't evaluate the function (x^115/e^x) at all points. That seems very
strange to me, although maybe it's running up against the
maximum size that floats can do -- but the plot looks fine, so maybe
not?
Dan
--
--- Dan Drake
----- http://math.pugetsound.edu/~ddrake
-------
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kcrisman
Feb 28, 2013, 9:06:45 PM2/28/13
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I would think this is a matplotlib issue that we are encountering - after all, the error is about 1e+12, or a trillion, so maybe there is something about how we are passing the tick marks on. David, can you give the *exact* command?
- kcrisman
David Smith
Mar 1, 2013, 10:59:05 AM3/1/13
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I'm going to explore this a little more and either post the code or a retraction. I found (after posting), when I put that function into a different graphing interact, that I could push it much farther without failure. So it may have been some less obvious error in the one I was writing. More later. Thanks, guys.
David Smith
Mar 1, 2013, 12:46:05 PM3/1/13
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I have attached a "graphing calculator" file in which the problem occurs. When I change the function to x^15/e^x and the range from 0 to 30, everything is fine. When I change the 15 to 16, I get the error messages pasted in below. Sorry about the length, but it's a complete mystery to me, so I don't want to leave anything out. Thanks.
--------------------------------------------------------------------------- ParseFatalException Traceback (most recent call last) <ipython-input-9-7fa122be4bfd> in <module>() ----> 1 sys._sage_.update_interact("ae9084fe-29e6-49b0-bdb6-83a8912c32ba",{"auto_update":True,"x_range":[[u"0",u"30",],],"f":u"x^16/e^x"}) /sagenb/sagecell-hood/sagecell/interact_sagecell.py in update_interact(interact_id, control_vals) 89 if c.preserve_state: 90 interact_info["state"][var]=kwargs[var] ---> 91 __interacts[interact_id]["function"](control_vals=kwargs) 92 93 /sagenb/sagecell-hood/sagecell/interact_sagecell.py in adapted_f(control_vals) 236 def adapted_f(control_vals): 237 with session_metadata({'interact_id': interact_id}): --> 238 returned=f(**control_vals) 239 return returned 240 # update global __interacts <ipython-input-1-a3966c085f34> in _(f, x_range, auto_update) 8 html("\[ f (x) = %s \]"%str(latex(f)) ) 9 p1=plot(f, (x,a,b), color='blue', legend_label='$f(x)$', axes_labels=['$x$','$y$'],tick_formatter="latex") ---> 10 show(p1, figsize=Integer(6)) /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/sage/misc/functional.pyc in show(x, *args, **kwds) 1597 if not isinstance(x, (sage.interfaces.expect.Expect, sage.interfaces.expect.ExpectElement)): 1598 try: -> 1599 return x.show(*args, **kwds) 1600 except AttributeError: 1601 pass /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/sage/misc/decorators.pyc in wrapper(*args, **kwds) 454 kwds[self.name + "options"] = suboptions 455 --> 456 return func(*args, **kwds) 457 458 #Add the options specified by @options to the signature of the wrapped /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/sage/plot/graphics.pyc in show(self, **kwds) 1733 kwds.setdefault('filename', sage.misc.misc.graphics_filename()) 1734 filename=kwds['filename'] -> 1735 self.save(**kwds) 1736 if sage.misc.misc.EMBEDDED_MODE['frontend']=='sagecell': 1737 import sys /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/sage/misc/decorators.pyc in wrapper(*args, **kwds) 454 kwds[self.name + "options"] = suboptions 455 --> 456 return func(*args, **kwds) 457 458 #Add the options specified by @options to the signature of the wrapped /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/sage/plot/graphics.pyc in save(self, filename, **kwds) 2608 2609 # tight_layout adjusts the *subplot* parameters so ticks aren't cut off, etc. -> 2610 figure.tight_layout() 2611 2612 if fig_tight is True: /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/matplotlib/figure.py in tight_layout(self, renderer, pad, h_pad, w_pad) 1389 subplot_list=subplot_list, 1390 ax_bbox_list=ax_bbox_list, -> 1391 pad=pad, h_pad=h_pad, w_pad=w_pad) 1392 1393 self.subplots_adjust(**kwargs) /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/matplotlib/tight_layout.py in auto_adjust_subplotpars(fig, renderer, nrows_ncols, num1num2_list, subplot_list, ax_bbox_list, pad, h_pad, w_pad, rect) 115 #ax_bbox = union([ax.get_position(original=True) for ax in subplots]) 116 --> 117 tight_bbox_raw = union([ax.get_tightbbox(renderer) for ax in subplots]) 118 tight_bbox = TransformedBbox(tight_bbox_raw, fig.transFigure.inverted()) 119 /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/matplotlib/axes.py in get_tightbbox(self, renderer, call_axes_locator) 8278 if bb_xaxis: bb.append(bb_xaxis) 8279 -> 8280 bb_yaxis = self.yaxis.get_tightbbox(renderer) 8281 if bb_yaxis: bb.append(bb_yaxis) 8282 /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/matplotlib/axis.py in get_tightbbox(self, renderer) 1001 1002 ticks_to_draw = self._update_ticks(renderer) -> 1003 ticklabelBoxes, ticklabelBoxes2 = self._get_tick_bboxes(ticks_to_draw, renderer) 1004 1005 self._update_label_position(ticklabelBoxes, ticklabelBoxes2) /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/matplotlib/axis.py in _get_tick_bboxes(self, ticks, renderer) 986 for tick in ticks: 987 if tick.label1On and tick.label1.get_visible(): --> 988 extent = tick.label1.get_window_extent(renderer) 989 ticklabelBoxes.append(extent) 990 if tick.label2On and tick.label2.get_visible(): /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/matplotlib/text.py in get_window_extent(self, renderer, dpi) 745 raise RuntimeError('Cannot get window extent w/o renderer') 746 --> 747 bbox, info = self._get_layout(self._renderer) 748 x, y = self.get_position() 749 x, y = self.get_transform().transform_point((x, y)) /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/matplotlib/text.py in _get_layout(self, renderer) 307 w, h, d = get_text_width_height_descent(clean_line, 308 self._fontproperties, --> 309 ismath=ismath) 310 else: 311 w, h, d = 0, 0, 0 /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/matplotlib/backends/backend_agg.py in get_text_width_height_descent(self, s, prop, ismath) 177 if ismath: 178 ox, oy, width, height, descent, fonts, used_characters = \ --> 179 self.mathtext_parser.parse(s, self.dpi, prop) 180 return width, height, descent 181 /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/matplotlib/mathtext.py in parse(self, s, dpi, prop) 2972 self.__class__._parser = Parser() 2973 -> 2974 box = self._parser.parse(s, font_output, fontsize, dpi) 2975 font_output.set_canvas_size(box.width, box.height, box.depth) 2976 result = font_output.get_results(box) /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/matplotlib/mathtext.py in parse(self, s, fonts_object, fontsize, dpi) 2350 self._state_stack = [self.State(fonts_object, 'default', 'rm', fontsize, dpi)] 2351 try: -> 2352 self._expression.parseString(s) 2353 except ParseException, err: 2354 raise ValueError("\n".join([ /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/matplotlib/pyparsing.py in parseString(self, instring, parseAll) 1046 if not self.keepTabs: 1047 instring = instring.expandtabs() -> 1048 loc, tokens = self._parse( instring, 0 ) 1049 if parseAll: 1050 StringEnd()._parse( instring, loc ) /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/matplotlib/pyparsing.py in _parseCache(self, instring, loc, doActions, callPreParse) 979 else: 980 try: --> 981 value = self._parseNoCache( instring, loc, doActions, callPreParse ) 982 ParserElement._exprArgCache[ lookup ] = (value[0],value[1].copy()) 983 return value /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/matplotlib/pyparsing.py in _parseNoCache(self, instring, loc, doActions, callPreParse) 922 if self.mayIndexError or loc >= len(instring): 923 try: --> 924 loc,tokens = self.parseImpl( instring, preloc, doActions ) 925 except IndexError: 926 raise ParseException( instring, len(instring), self.errmsg, self ) /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/matplotlib/pyparsing.py in parseImpl(self, instring, loc, doActions) 2557 def parseImpl( self, instring, loc, doActions=True ): 2558 if self.expr is not None: -> 2559 return self.expr._parse( instring, loc, doActions, callPreParse=False ) 2560 else: 2561 raise ParseException("",loc,self.errmsg,self) /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/matplotlib/pyparsing.py in _parseCache(self, instring, loc, doActions, callPreParse) 979 else: 980 try: --> 981 value = self._parseNoCache( instring, loc, doActions, callPreParse ) 982 ParserElement._exprArgCache[ lookup ] = (value[0],value[1].copy()) 983 return value /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/matplotlib/pyparsing.py in _parseNoCache(self, instring, loc, doActions, callPreParse) 922 if self.mayIndexError or loc >= len(instring): 923 try: --> 924 loc,tokens = self.parseImpl( instring, preloc, doActions ) 925 except IndexError: 926 raise ParseException( instring, len(instring), self.errmsg, self ) /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/matplotlib/pyparsing.py in parseImpl(self, instring, loc, doActions) 2305 raise ParseSyntaxException( ParseException(instring, len(instring), self.errmsg, self) ) 2306 else: -> 2307 loc, exprtokens = e._parse( instring, loc, doActions ) 2308 if exprtokens or exprtokens.keys(): 2309 resultlist += exprtokens /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/matplotlib/pyparsing.py in _parseCache(self, instring, loc, doActions, callPreParse) 979 else: 980 try: --> 981 value = self._parseNoCache( instring, loc, doActions, callPreParse ) 982 ParserElement._exprArgCache[ lookup ] = (value[0],value[1].copy()) 983 return value /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/matplotlib/pyparsing.py in _parseNoCache(self, instring, loc, doActions, callPreParse) 922 if self.mayIndexError or loc >= len(instring): 923 try: --> 924 loc,tokens = self.parseImpl( instring, preloc, doActions ) 925 except IndexError: 926 raise ParseException( instring, len(instring), self.errmsg, self ) /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/matplotlib/pyparsing.py in parseImpl(self, instring, loc, doActions) 2670 tokens = [] 2671 try: -> 2672 loc, tokens = self.expr._parse( instring, loc, doActions, callPreParse=False ) 2673 hasIgnoreExprs = ( len(self.ignoreExprs) > 0 ) 2674 while 1: /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/matplotlib/pyparsing.py in _parseCache(self, instring, loc, doActions, callPreParse) 979 else: 980 try: --> 981 value = self._parseNoCache( instring, loc, doActions, callPreParse ) 982 ParserElement._exprArgCache[ lookup ] = (value[0],value[1].copy()) 983 return value /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/matplotlib/pyparsing.py in _parseNoCache(self, instring, loc, doActions, callPreParse) 922 if self.mayIndexError or loc >= len(instring): 923 try: --> 924 loc,tokens = self.parseImpl( instring, preloc, doActions ) 925 except IndexError: 926 raise ParseException( instring, len(instring), self.errmsg, self ) /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/matplotlib/pyparsing.py in parseImpl(self, instring, loc, doActions) 2305 raise ParseSyntaxException( ParseException(instring, len(instring), self.errmsg, self) ) 2306 else: -> 2307 loc, exprtokens = e._parse( instring, loc, doActions ) 2308 if exprtokens or exprtokens.keys(): 2309 resultlist += exprtokens /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/matplotlib/pyparsing.py in _parseCache(self, instring, loc, doActions, callPreParse) 979 else: 980 try: --> 981 value = self._parseNoCache( instring, loc, doActions, callPreParse ) 982 ParserElement._exprArgCache[ lookup ] = (value[0],value[1].copy()) 983 return value /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/matplotlib/pyparsing.py in _parseNoCache(self, instring, loc, doActions, callPreParse) 922 if self.mayIndexError or loc >= len(instring): 923 try: --> 924 loc,tokens = self.parseImpl( instring, preloc, doActions ) 925 except IndexError: 926 raise ParseException( instring, len(instring), self.errmsg, self ) /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/matplotlib/pyparsing.py in parseImpl(self, instring, loc, doActions) 2414 for e in self.exprs: 2415 try: -> 2416 ret = e._parse( instring, loc, doActions ) 2417 return ret 2418 except ParseException, err: /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/matplotlib/pyparsing.py in _parseCache(self, instring, loc, doActions, callPreParse) 979 else: 980 try: --> 981 value = self._parseNoCache( instring, loc, doActions, callPreParse ) 982 ParserElement._exprArgCache[ lookup ] = (value[0],value[1].copy()) 983 return value /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/matplotlib/pyparsing.py in _parseNoCache(self, instring, loc, doActions, callPreParse) 948 else: 949 for fn in self.parseAction: --> 950 tokens = fn( instring, tokensStart, retTokens ) 951 if tokens is not None: 952 retTokens = ParseResults( tokens, /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/matplotlib/mathtext.py in raise_error(s, loc, toks) 2047 """ 2048 def raise_error(s, loc, toks): -> 2049 raise ParseFatalException(msg + "\n" + s) 2050 2051 empty = Empty()
ParseFatalException: Expected end of math '$'
$\verb|1e+12|$ (at char 0), (line:1, col:1)--------------------------------------------------------------------------- ParseFatalException Traceback (most recent call last) <ipython-input-9-7fa122be4bfd> in <module>() ----> 1 sys._sage_.update_interact("ae9084fe-29e6-49b0-bdb6-83a8912c32ba",{"auto_update":True,"x_range":[[u"0",u"30",],],"f":u"x^16/e^x"}) /sagenb/sagecell-hood/sagecell/interact_sagecell.py in update_interact(interact_id, control_vals) 89 if c.preserve_state: 90 interact_info["state"][var]=kwargs[var] ---> 91 __interacts[interact_id]["function"](control_vals=kwargs) 92 93 /sagenb/sagecell-hood/sagecell/interact_sagecell.py in adapted_f(control_vals) 236 def adapted_f(control_vals): 237 with session_metadata({'interact_id': interact_id}): --> 238 returned=f(**control_vals) 239 return returned 240 # update global __interacts <ipython-input-1-a3966c085f34> in _(f, x_range, auto_update) 8 html("\[ f (x) = %s \]"%str(latex(f)) ) 9 p1=plot(f, (x,a,b), color='blue', legend_label='$f(x)$', axes_labels=['$x$','$y$'],tick_formatter="latex") ---> 10 show(p1, figsize=Integer(6)) /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/sage/misc/functional.pyc in show(x, *args, **kwds) 1597 if not isinstance(x, (sage.interfaces.expect.Expect, sage.interfaces.expect.ExpectElement)): 1598 try: -> 1599 return x.show(*args, **kwds) 1600 except AttributeError: 1601 pass /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/sage/misc/decorators.pyc in wrapper(*args, **kwds) 454 kwds[self.name + "options"] = suboptions 455 --> 456 return func(*args, **kwds) 457 458 #Add the options specified by @options to the signature of the wrapped /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/sage/plot/graphics.pyc in show(self, **kwds) 1733 kwds.setdefault('filename', sage.misc.misc.graphics_filename()) 1734 filename=kwds['filename'] -> 1735 self.save(**kwds) 1736 if sage.misc.misc.EMBEDDED_MODE['frontend']=='sagecell': 1737 import sys /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/sage/misc/decorators.pyc in wrapper(*args, **kwds) 454 kwds[self.name + "options"] = suboptions 455 --> 456 return func(*args, **kwds) 457 458 #Add the options specified by @options to the signature of the wrapped /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/sage/plot/graphics.pyc in save(self, filename, **kwds) 2608 2609 # tight_layout adjusts the *subplot* parameters so ticks aren't cut off, etc. -> 2610 figure.tight_layout() 2611 2612 if fig_tight is True: /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/matplotlib/figure.py in tight_layout(self, renderer, pad, h_pad, w_pad) 1389 subplot_list=subplot_list, 1390 ax_bbox_list=ax_bbox_list, -> 1391 pad=pad, h_pad=h_pad, w_pad=w_pad) 1392 1393 self.subplots_adjust(**kwargs) /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/matplotlib/tight_layout.py in auto_adjust_subplotpars(fig, renderer, nrows_ncols, num1num2_list, subplot_list, ax_bbox_list, pad, h_pad, w_pad, rect) 115 #ax_bbox = union([ax.get_position(original=True) for ax in subplots]) 116 --> 117 tight_bbox_raw = union([ax.get_tightbbox(renderer) for ax in subplots]) 118 tight_bbox = TransformedBbox(tight_bbox_raw, fig.transFigure.inverted()) 119 /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/matplotlib/axes.py in get_tightbbox(self, renderer, call_axes_locator) 8278 if bb_xaxis: bb.append(bb_xaxis) 8279 -> 8280 bb_yaxis = self.yaxis.get_tightbbox(renderer) 8281 if bb_yaxis: bb.append(bb_yaxis) 8282 /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/matplotlib/axis.py in get_tightbbox(self, renderer) 1001 1002 ticks_to_draw = self._update_ticks(renderer) -> 1003 ticklabelBoxes, ticklabelBoxes2 = self._get_tick_bboxes(ticks_to_draw, renderer) 1004 1005 self._update_label_position(ticklabelBoxes, ticklabelBoxes2) /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/matplotlib/axis.py in _get_tick_bboxes(self, ticks, renderer) 986 for tick in ticks: 987 if tick.label1On and tick.label1.get_visible(): --> 988 extent = tick.label1.get_window_extent(renderer) 989 ticklabelBoxes.append(extent) 990 if tick.label2On and tick.label2.get_visible(): /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/matplotlib/text.py in get_window_extent(self, renderer, dpi) 745 raise RuntimeError('Cannot get window extent w/o renderer') 746 --> 747 bbox, info = self._get_layout(self._renderer) 748 x, y = self.get_position() 749 x, y = self.get_transform().transform_point((x, y)) /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/matplotlib/text.py in _get_layout(self, renderer) 307 w, h, d = get_text_width_height_descent(clean_line, 308 self._fontproperties, --> 309 ismath=ismath) 310 else: 311 w, h, d = 0, 0, 0 /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/matplotlib/backends/backend_agg.py in get_text_width_height_descent(self, s, prop, ismath) 177 if ismath: 178 ox, oy, width, height, descent, fonts, used_characters = \ --> 179 self.mathtext_parser.parse(s, self.dpi, prop) 180 return width, height, descent 181 /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/matplotlib/mathtext.py in parse(self, s, dpi, prop) 2972 self.__class__._parser = Parser() 2973 -> 2974 box = self._parser.parse(s, font_output, fontsize, dpi) 2975 font_output.set_canvas_size(box.width, box.height, box.depth) 2976 result = font_output.get_results(box) /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/matplotlib/mathtext.py in parse(self, s, fonts_object, fontsize, dpi) 2350 self._state_stack = [self.State(fonts_object, 'default', 'rm', fontsize, dpi)] 2351 try: -> 2352 self._expression.parseString(s) 2353 except ParseException, err: 2354 raise ValueError("\n".join([ /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/matplotlib/pyparsing.py in parseString(self, instring, parseAll) 1046 if not self.keepTabs: 1047 instring = instring.expandtabs() -> 1048 loc, tokens = self._parse( instring, 0 ) 1049 if parseAll: 1050 StringEnd()._parse( instring, loc ) /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/matplotlib/pyparsing.py in _parseCache(self, instring, loc, doActions, callPreParse) 979 else: 980 try: --> 981 value = self._parseNoCache( instring, loc, doActions, callPreParse ) 982 ParserElement._exprArgCache[ lookup ] = (value[0],value[1].copy()) 983 return value /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/matplotlib/pyparsing.py in _parseNoCache(self, instring, loc, doActions, callPreParse) 922 if self.mayIndexError or loc >= len(instring): 923 try: --> 924 loc,tokens = self.parseImpl( instring, preloc, doActions ) 925 except IndexError: 926 raise ParseException( instring, len(instring), self.errmsg, self ) /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/matplotlib/pyparsing.py in parseImpl(self, instring, loc, doActions) 2557 def parseImpl( self, instring, loc, doActions=True ): 2558 if self.expr is not None: -> 2559 return self.expr._parse( instring, loc, doActions, callPreParse=False ) 2560 else: 2561 raise ParseException("",loc,self.errmsg,self) /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/matplotlib/pyparsing.py in _parseCache(self, instring, loc, doActions, callPreParse) 979 else: 980 try: --> 981 value = self._parseNoCache( instring, loc, doActions, callPreParse ) 982 ParserElement._exprArgCache[ lookup ] = (value[0],value[1].copy()) 983 return value /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/matplotlib/pyparsing.py in _parseNoCache(self, instring, loc, doActions, callPreParse) 922 if self.mayIndexError or loc >= len(instring): 923 try: --> 924 loc,tokens = self.parseImpl( instring, preloc, doActions ) 925 except IndexError: 926 raise ParseException( instring, len(instring), self.errmsg, self ) /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/matplotlib/pyparsing.py in parseImpl(self, instring, loc, doActions) 2305 raise ParseSyntaxException( ParseException(instring, len(instring), self.errmsg, self) ) 2306 else: -> 2307 loc, exprtokens = e._parse( instring, loc, doActions ) 2308 if exprtokens or exprtokens.keys(): 2309 resultlist += exprtokens /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/matplotlib/pyparsing.py in _parseCache(self, instring, loc, doActions, callPreParse) 979 else: 980 try: --> 981 value = self._parseNoCache( instring, loc, doActions, callPreParse ) 982 ParserElement._exprArgCache[ lookup ] = (value[0],value[1].copy()) 983 return value /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/matplotlib/pyparsing.py in _parseNoCache(self, instring, loc, doActions, callPreParse) 922 if self.mayIndexError or loc >= len(instring): 923 try: --> 924 loc,tokens = self.parseImpl( instring, preloc, doActions ) 925 except IndexError: 926 raise ParseException( instring, len(instring), self.errmsg, self ) /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/matplotlib/pyparsing.py in parseImpl(self, instring, loc, doActions) 2670 tokens = [] 2671 try: -> 2672 loc, tokens = self.expr._parse( instring, loc, doActions, callPreParse=False ) 2673 hasIgnoreExprs = ( len(self.ignoreExprs) > 0 ) 2674 while 1: /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/matplotlib/pyparsing.py in _parseCache(self, instring, loc, doActions, callPreParse) 979 else: 980 try: --> 981 value = self._parseNoCache( instring, loc, doActions, callPreParse ) 982 ParserElement._exprArgCache[ lookup ] = (value[0],value[1].copy()) 983 return value /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/matplotlib/pyparsing.py in _parseNoCache(self, instring, loc, doActions, callPreParse) 922 if self.mayIndexError or loc >= len(instring): 923 try: --> 924 loc,tokens = self.parseImpl( instring, preloc, doActions ) 925 except IndexError: 926 raise ParseException( instring, len(instring), self.errmsg, self ) /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/matplotlib/pyparsing.py in parseImpl(self, instring, loc, doActions) 2305 raise ParseSyntaxException( ParseException(instring, len(instring), self.errmsg, self) ) 2306 else: -> 2307 loc, exprtokens = e._parse( instring, loc, doActions ) 2308 if exprtokens or exprtokens.keys(): 2309 resultlist += exprtokens /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/matplotlib/pyparsing.py in _parseCache(self, instring, loc, doActions, callPreParse) 979 else: 980 try: --> 981 value = self._parseNoCache( instring, loc, doActions, callPreParse ) 982 ParserElement._exprArgCache[ lookup ] = (value[0],value[1].copy()) 983 return value /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/matplotlib/pyparsing.py in _parseNoCache(self, instring, loc, doActions, callPreParse) 922 if self.mayIndexError or loc >= len(instring): 923 try: --> 924 loc,tokens = self.parseImpl( instring, preloc, doActions ) 925 except IndexError: 926 raise ParseException( instring, len(instring), self.errmsg, self ) /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/matplotlib/pyparsing.py in parseImpl(self, instring, loc, doActions) 2414 for e in self.exprs: 2415 try: -> 2416 ret = e._parse( instring, loc, doActions ) 2417 return ret 2418 except ParseException, err: /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/matplotlib/pyparsing.py in _parseCache(self, instring, loc, doActions, callPreParse) 979 else: 980 try: --> 981 value = self._parseNoCache( instring, loc, doActions, callPreParse ) 982 ParserElement._exprArgCache[ lookup ] = (value[0],value[1].copy()) 983 return value /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/matplotlib/pyparsing.py in _parseNoCache(self, instring, loc, doActions, callPreParse) 948 else: 949 for fn in self.parseAction: --> 950 tokens = fn( instring, tokensStart, retTokens ) 951 if tokens is not None: 952 retTokens = ParseResults( tokens, /sagenb/sagecell-hood/sage-5.3-sage.math.washington.edu-x86_64-Linux/local/lib/python2.7/site-packages/matplotlib/mathtext.py in raise_error(s, loc, toks) 2047 """ 2048 def raise_error(s, loc, toks): -> 2049 raise ParseFatalException(msg + "\n" + s) 2050 2051 empty = Empty()
ParseFatalException: Expected end of math '$'
$\verb|1e+12|$ (at char 0), (line:1, col:1)Powered by 
sage-graphing-calculator-f(x).html
kcrisman
Mar 1, 2013, 2:02:21 PM3/1/13
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For reference,
x = var("x")
@interact
def _(f = input_box(x, label='$f(x) = $', width=40), x_range=input_grid(1,2,[[-8,8]], label='$x$ range', width=10), auto_update=False):
a,b=x_range[0]
html("\[ f (x) = %s \]"%str(latex(f)) )
p1=plot(f, (x,a,b), color='blue', legend_label='$f(x)$', axes_labels=['$x$','$y$'],tick_formatter="latex")
show(p1, figsize=6)
Jason Grout
Mar 1, 2013, 2:06:54 PM3/1/13
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This looks like possibly a bug in matplotlib.
Thanks,
Jason
David Smith
Mar 2, 2013, 4:04:51 PM3/2/13
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Thanks, Jason. I never would have thought of that, but on reflection, it appeared that the latex formatter would never switch to scientific notation, and this is a case where you definitely want it. I suppose the error was when it ran out of room for all those digits. With that removed, Sage is perfectly happy to graph x^100/e^x.
David
David
John Travis
Mar 6, 2013, 3:55:58 PM3/6/13
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Just for the fun of it, I was playing with:
@interact
def _(m=slider(1,250,1,1)):
plot(x^m/e^x,(x,0,2*m)).show()
and things work really nice till m = 128. After that, it still runs but the graph has horizontal issues--using either aleph or 5.5.
JT
David Smith
Mar 19, 2013, 5:30:59 PM3/19/13
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I like this even better that what I was doing for the intended illustration in our book. The URL is https://www.math.duke.edu/education/calculustext-rev11/Chapter10/Section10-3/Chapter10-3-3M.html and the interact is at the very bottom of the page. Thanks, John.
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