strange sum error

Martin R

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Feb 5, 2019, 11:00:47 AM2/5/19

to FriCAS - computer algebra system

I think I found something rather strange:

(1) -> sum(sum(a^k, a=1..k), k=1..n)

- log(%C)

>> Error detected within library code:

Hidden constant detected

Best,

Martin

Riccardo GUIDA

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Feb 5, 2019, 2:19:52 PM2/5/19

to fricas...@googlegroups.com

Reproduced in 1.3.4
ric
PS btw thanks Waldek and you all for 1.3.5

FriCAS Computer Algebra System
Version: FriCAS 1.3.4
Timestamp: Wed Jun 27 13:40:07 CEST 2018
-----------------------------------------------------------------------------
Issue )copyright to view copyright notices.
Issue )summary for a summary of useful system commands.
Issue )quit to leave FriCAS and return to shell.
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Type: Void

(1) -> sum(sum(a^k, a=1..k), k=1..n)
- log(%C)

>> Error detected within library code:
Hidden constant detected

(1) -> sum(sum(a^k, a=1..k), k=1..10)

- log(%C)

>> Error detected within library code:
Hidden constant detected

(1) -> sum(a^k, a=1..k)

k
──┐ k
(1) > a
──┘
a = 1
Type: Expression(Integer)
(2) -> f(k)==sum(a^k, a=1..k)
Type: Void
(3) -> sum(f(k), k=1..n)
Compiling function f with type Variable(k) -> Expression(Integer)

- log(%C)

>> Error detected within library code:
Hidden constant detected

(3) -> f(3)
Compiling function f with type PositiveInteger -> Fraction(
Polynomial(Integer))

(3) 36
Type: Fraction(Polynomial(Integer))
(4) ->

Martin R

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Feb 18, 2019, 4:14:41 PM2/18/19

to FriCAS - computer algebra system

Here is a simplification of the problem:

(1) -> ex := sum(a^k,a=1..k); ex1 := ex/eval(ex, k=k-1);

Type: Expression(Integer)

(2) -> )tr EFSTRUC )math

Packages traced:

ElementaryFunctionStructurePackage(Integer,Expression(

Integer))

Parameterized constructors traced:

EFSTRUC

(2) -> normalize(ex1)

1<enter ElementaryFunctionStructurePackage.normalize,192 :

k

--+ k

> a

--+

a = 1

arg1 = -------------

k - 1

--+ k - 1

> a

--+

a = 1

1<enter ElementaryFunctionStructurePackage.normalize,191 :

k

--+ k

> a

--+

a = 1

arg1 = [-------------]

k - 1

--+ k - 1

> a

--+

a = 1

arg2 = []

1<enter ElementaryFunctionStructurePackage.realElementary,23 :

k

--+ k

> a

--+

a = 1

arg1 = -------------

k - 1

--+ k - 1

> a

--+

a = 1

1<enter ElementaryFunctionStructurePackage.rmap,18 :

arg1 = theMap(EFSTRUC;realElem!0,655)

k

--+ k

> a

--+

a = 1

arg2 = -------------

k - 1

--+ k - 1

> a

--+

a = 1

2<enter ElementaryFunctionStructurePackage.rmap,18 :

arg1 = theMap(EFSTRUC;realElem!0,655)

k

arg2 = %C

3<enter ElementaryFunctionStructurePackage.rmap,18 :

arg1 = theMap(EFSTRUC;realElem!0,655)

arg2 = %C

3>exit ElementaryFunctionStructurePackage.rmap,18 :

%C

3<enter ElementaryFunctionStructurePackage.rmap,18 :

arg1 = theMap(EFSTRUC;realElem!0,655)

arg2 = k

3>exit ElementaryFunctionStructurePackage.rmap,18 :

k

2>exit ElementaryFunctionStructurePackage.rmap,18 :

k log(%C)

%e

2<enter ElementaryFunctionStructurePackage.rmap,18 :

arg1 = theMap(EFSTRUC;realElem!0,655)

arg2 = %C

2>exit ElementaryFunctionStructurePackage.rmap,18 :

%C

2<enter ElementaryFunctionStructurePackage.rmap,18 :

arg1 = theMap(EFSTRUC;realElem!0,655)

arg2 = a

2>exit ElementaryFunctionStructurePackage.rmap,18 :

a

2<enter ElementaryFunctionStructurePackage.rmap,18 :

arg1 = theMap(EFSTRUC;realElem!0,655)

arg2 = 1

2>exit ElementaryFunctionStructurePackage.rmap,18 :

1

2<enter ElementaryFunctionStructurePackage.rmap,18 :

arg1 = theMap(EFSTRUC;realElem!0,655)

arg2 = k

2>exit ElementaryFunctionStructurePackage.rmap,18 :

k

2<enter ElementaryFunctionStructurePackage.rmap,18 :

arg1 = theMap(EFSTRUC;realElem!0,655)

k - 1

arg2 = %C

3<enter ElementaryFunctionStructurePackage.rmap,18 :

arg1 = theMap(EFSTRUC;realElem!0,655)

arg2 = %C

3>exit ElementaryFunctionStructurePackage.rmap,18 :

%C

3<enter ElementaryFunctionStructurePackage.rmap,18 :

arg1 = theMap(EFSTRUC;realElem!0,655)

arg2 = k - 1

3>exit ElementaryFunctionStructurePackage.rmap,18 :

k - 1

2>exit ElementaryFunctionStructurePackage.rmap,18 :

(k - 1)log(%C)

%e

2<enter ElementaryFunctionStructurePackage.rmap,18 :

arg1 = theMap(EFSTRUC;realElem!0,655)

arg2 = %C

2>exit ElementaryFunctionStructurePackage.rmap,18 :

%C

2<enter ElementaryFunctionStructurePackage.rmap,18 :

arg1 = theMap(EFSTRUC;realElem!0,655)

arg2 = a

2>exit ElementaryFunctionStructurePackage.rmap,18 :

a

2<enter ElementaryFunctionStructurePackage.rmap,18 :

arg1 = theMap(EFSTRUC;realElem!0,655)

arg2 = 1

2>exit ElementaryFunctionStructurePackage.rmap,18 :

1

2<enter ElementaryFunctionStructurePackage.rmap,18 :

arg1 = theMap(EFSTRUC;realElem!0,655)

arg2 = k - 1

2>exit ElementaryFunctionStructurePackage.rmap,18 :

k - 1

1>exit ElementaryFunctionStructurePackage.rmap,18 :

k

--+ k log(a)

> %e

--+

a = 1

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

k - 1

--+ (k - 1)log(a)

> %e

--+

a = 1

1>exit ElementaryFunctionStructurePackage.realElementary,23 :

k

--+ k log(a)

> %e

--+

a = 1

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

k - 1

--+ (k - 1)log(a)

> %e

--+

a = 1

1<enter ElementaryFunctionStructurePackage.rischNormalize,174 :

k

--+ k log(a)

> %e

--+

a = 1

arg1 = [----------------------]

k - 1

--+ (k - 1)log(a)

> %e

--+

a = 1

arg2 = []

2<enter ElementaryFunctionStructurePackage.rischNormalize,174 :

k

--+ k log(a)

> %e

--+

a = 1

arg1 = [---------------------------]

k - 1

--+ - log(a) k log(a)

> %e %e

--+

a = 1

arg2 = []

- log(%C)

>> Error detected within library code:

Hidden constant detected

(2) ->

Martin R

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Feb 19, 2019, 2:39:52 PM2/19/19

to FriCAS - computer algebra system

Dear Waldek,

I'm afraid I cannot help much further. At first I thought that normalize might expect that the dummy variables in

sum(a^k, a=1..k) and eval(sum(a^k, a=1..k), k=k-1) should be different, but this doesn't help:

(1) -> ex := sum(a^k,a=1..k); ex2 := sum(a^(k-1),a=1..k-1);

Type: Expression(Integer)

(2) -> [tower kernels ex, tower kernels ex2]

k k - 1

k --+ k k - 1 --+ k - 1

(2) [[k, %C , > a ], [k, %D , > a ]]

--+ --+

a = 1 a = 1

Type: List(List(Kernel(Expression(Integer))))

(3) -> normalize(ex/ex2)

log(%D)

>> Error detected within library code:

Hidden constant detected

So, maybe normalize should somehow know that the dummy variables are dummy variables?

Martin

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