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May 1, 2010, 5:30:34 AM5/1/10

to ross kyprianou, sage-...@googlegroups.com

Dear Ross,

On Mon, Apr 19, 2010 at 06:38:31PM +0930, ross kyprianou wrote:

> (Im trying to finish this in 2-3 weeks to include some results in a

> paper but I understand that may not be possible)

Oops, I just noticed this deadline of yours; I hope you will still

make it! Please find attached a possible refactorisation of your code.

Here is a short extract of the doc (to be run after loading the code):

EXAMPLES::

sage: Alg = SymbolicMatrixAlgebra(QQ)

sage: A = Alg.matrix("A",3,2)

sage: B = Alg.matrix("B",2,3)

sage: C = Alg.matrix("C",2,3)

sage: D = Alg.matrix("D",3,3)

Example 1: Adding/Multiplying matrices of correct size::

sage: A * (B + C)

A B + A C

Example 2: Transposing a sum of matrices::

sage: (B + C).transpose()

C^t + B^t

Example 3: Transposing a product of matrices::

sage: (A * B).transpose()

B^t A^t

Example 4: Inverting a product of matrices::

sage: (A * B)^-1

B^-1 A^-1

Example 5: Multiplying by its inverse::

sage: D * D^-1 # todo: not implemented

I

Enjoy, and let me know how it goes!

Best,

Nicolas

--

Nicolas M. Thiéry "Isil" <nth...@users.sf.net>

http://Nicolas.Thiery.name/

--

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URL: http://www.sagemath.org

On Mon, Apr 19, 2010 at 06:38:31PM +0930, ross kyprianou wrote:

> (Im trying to finish this in 2-3 weeks to include some results in a

> paper but I understand that may not be possible)

Oops, I just noticed this deadline of yours; I hope you will still

make it! Please find attached a possible refactorisation of your code.

Here is a short extract of the doc (to be run after loading the code):

EXAMPLES::

sage: Alg = SymbolicMatrixAlgebra(QQ)

sage: A = Alg.matrix("A",3,2)

sage: B = Alg.matrix("B",2,3)

sage: C = Alg.matrix("C",2,3)

sage: D = Alg.matrix("D",3,3)

Example 1: Adding/Multiplying matrices of correct size::

sage: A * (B + C)

A B + A C

Example 2: Transposing a sum of matrices::

sage: (B + C).transpose()

C^t + B^t

Example 3: Transposing a product of matrices::

sage: (A * B).transpose()

B^t A^t

Example 4: Inverting a product of matrices::

sage: (A * B)^-1

B^-1 A^-1

Example 5: Multiplying by its inverse::

sage: D * D^-1 # todo: not implemented

I

Enjoy, and let me know how it goes!

Best,

Nicolas

--

Nicolas M. Thiéry "Isil" <nth...@users.sf.net>

http://Nicolas.Thiery.name/

--

To post to this group, send an email to sage-...@googlegroups.com

To unsubscribe from this group, send an email to sage-devel+...@googlegroups.com

For more options, visit this group at http://groups.google.com/group/sage-devel

URL: http://www.sagemath.org

May 1, 2010, 8:05:35 AM5/1/10

to sage-devel

Nicolas

No worries about deadlines - this looks excellent - thanks!

Will let you know how things go. This gives me lots to work with

Thanks again!

On May 1, 6:30 pm, "Nicolas M. Thiery" <Nicolas.Thi...@u-psud.fr>

wrote:

> Nicolas M. Thiéry "Isil" <nthi...@users.sf.net>http://Nicolas.Thiery.name/

> 6KViewDownload

No worries about deadlines - this looks excellent - thanks!

Will let you know how things go. This gives me lots to work with

Thanks again!

On May 1, 6:30 pm, "Nicolas M. Thiery" <Nicolas.Thi...@u-psud.fr>

wrote:

>

> --

> To post to this group, send an email to sage-...@googlegroups.com

> To unsubscribe from this group, send an email to sage-devel+...@googlegroups.com

> For more options, visit this group athttp://groups.google.com/group/sage-devel

> URL:http://www.sagemath.org

>

> matrix.sage
> --

> To post to this group, send an email to sage-...@googlegroups.com

> To unsubscribe from this group, send an email to sage-devel+...@googlegroups.com

> For more options, visit this group athttp://groups.google.com/group/sage-devel

> URL:http://www.sagemath.org

>

> 6KViewDownload

May 2, 2010, 3:09:09 AM5/2/10

to sage-devel

This turned out as good as it looked Nicolas

A lot of the planned functionality is already in place with this

initial code - Thanks!

Now it should be possible (for me) to implement some more code (which

is indicated in the second section

(below) i.e. under the section with title "I need to implement

these").

I studied matrix.sage and some of the python scripts in .../devel/sage/

sage/categories

I just need some guidance where to put new code or what to overload.

e.g. I tried to create a

def sum_on_basis(self, w1, w2):

under the code where I saw

def product_on_basis(self, w1, w2):

but that had no effect on the addition bug shown below.

Below, the working functionality is indicated first and below that is

the new work Ill do with

a little guidance. I think the coding I need to do is straight

forward.

The challenge should just be where to put the code associated each bug

below.

e.g. Ive written the fix to the sum bug below but

- do I put it in a _sum_( ) method?

- do I put it in a sum_on_basis(self, w1, w2) method?

- and where (or which class?) do I put these methods in?

Heres the results of some testing...

=====================================

Starting with these definitions...

sage: Alg = SymbolicMatrixAlgebra(QQ)

sage: A = Alg.matrix("A",3,2)

sage: B = Alg.matrix("B",2,3)

sage: C = Alg.matrix("C",2,3)

sage: D = Alg.matrix("D",3,3)

===================================

==== The following worked well ====

===================================

# Conformable matrix sizes for multiplication passes

sage: A*B

A B

sage: B*C.transpose()

B C^t

# Non-Conformable matrix sizes for multiplication is caught

sage: B*C

---------------------------------------------------------------------------

AssertionError Traceback (most recent call

last)

...

AssertionError: Non-conformable matrices: matrix sizes are

incompatible for multiplication

# Additive inverse

sage: D-D

0

#Additive identity (no probs with sizes is intuitively ok)

sage: A+0

A

# Conformable matrix sizes for addition passes

sage: B+C

B + C

# transposes

sage: A.transpose()

A^t

sage: (A+B).transpose()

A^t + B^t

# only square matrices have an inverse (we'll think about pseudo-

inverses later)

sage: ~A

---------------------------------------------------------------------------

AssertionError Traceback (most recent call

last)

...

AssertionError: Can't inverse non square matrix

=====================================

==== I need to implement these ====

=====================================

# Non-Conformable matrix sizes for addition is *NOT* caught

# (Also need to change the unusual reversal of order being printed)

# QUESTION

sage: A+B

B + A

# simplify multiplicative inverse (i.e. return I but not the one from

the symbolic ring)

sage: ~D*D

D^-1 D

# allow ~(A*B) to work (currently crashes with size error because Ive

specified this should be returned as B^-1 A^-1 and neither are square:

but A*B is square so ~(A*B) should return (A*B)^-1 "unsimplified" -

later we can introduce assume(A*B,'invertible')

sage: ~(A*B)

# multiplying by identity (question of size of I arises - see additive

identity example above)

sage: D*I

D

===============================

==== Probably these too ====

===============================

# (a) ~~D returns D but ~~D == D returns false (confusing) i.e.

sage: ~~D

D

sage: ~~D == D

False

# (b) define _pow_() so D^-1 returns ~D

cheers!

A lot of the planned functionality is already in place with this

initial code - Thanks!

Now it should be possible (for me) to implement some more code (which

is indicated in the second section

(below) i.e. under the section with title "I need to implement

these").

I studied matrix.sage and some of the python scripts in .../devel/sage/

sage/categories

I just need some guidance where to put new code or what to overload.

e.g. I tried to create a

def sum_on_basis(self, w1, w2):

under the code where I saw

def product_on_basis(self, w1, w2):

but that had no effect on the addition bug shown below.

Below, the working functionality is indicated first and below that is

the new work Ill do with

a little guidance. I think the coding I need to do is straight

forward.

The challenge should just be where to put the code associated each bug

below.

e.g. Ive written the fix to the sum bug below but

- do I put it in a _sum_( ) method?

- do I put it in a sum_on_basis(self, w1, w2) method?

- and where (or which class?) do I put these methods in?

Heres the results of some testing...

=====================================

Starting with these definitions...

sage: Alg = SymbolicMatrixAlgebra(QQ)

sage: A = Alg.matrix("A",3,2)

sage: B = Alg.matrix("B",2,3)

sage: C = Alg.matrix("C",2,3)

sage: D = Alg.matrix("D",3,3)

==== The following worked well ====

===================================

# Conformable matrix sizes for multiplication passes

sage: A*B

A B

sage: B*C.transpose()

B C^t

# Non-Conformable matrix sizes for multiplication is caught

sage: B*C

---------------------------------------------------------------------------

AssertionError Traceback (most recent call

last)

...

AssertionError: Non-conformable matrices: matrix sizes are

incompatible for multiplication

# Additive inverse

sage: D-D

0

#Additive identity (no probs with sizes is intuitively ok)

sage: A+0

A

# Conformable matrix sizes for addition passes

sage: B+C

B + C

# transposes

sage: A.transpose()

A^t

sage: (A+B).transpose()

A^t + B^t

# only square matrices have an inverse (we'll think about pseudo-

inverses later)

sage: ~A

---------------------------------------------------------------------------

AssertionError Traceback (most recent call

last)

...

AssertionError: Can't inverse non square matrix

=====================================

==== I need to implement these ====

=====================================

# Non-Conformable matrix sizes for addition is *NOT* caught

# (Also need to change the unusual reversal of order being printed)

# QUESTION

sage: A+B

B + A

# simplify multiplicative inverse (i.e. return I but not the one from

the symbolic ring)

sage: ~D*D

D^-1 D

# allow ~(A*B) to work (currently crashes with size error because Ive

specified this should be returned as B^-1 A^-1 and neither are square:

but A*B is square so ~(A*B) should return (A*B)^-1 "unsimplified" -

later we can introduce assume(A*B,'invertible')

sage: ~(A*B)

# multiplying by identity (question of size of I arises - see additive

identity example above)

sage: D*I

D

===============================

==== Probably these too ====

===============================

# (a) ~~D returns D but ~~D == D returns false (confusing) i.e.

sage: ~~D

D

sage: ~~D == D

False

# (b) define _pow_() so D^-1 returns ~D

cheers!

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