Opened 8 months ago

Last modified 8 months ago

#25520 new defect

Wrong 0th symbolic power of a matrix

Reported by: tmonteil Owned by:
Priority: major Milestone: sage-8.3
Component: symbolics Keywords:
Cc: mforets, slelievre Merged in:
Authors: Reviewers:
Report Upstream: N/A Work issues:
Branch: Commit:
Dependencies: Stopgaps:

Description

From this ask question, the symbolic power of a matrix gives a result that is correct when restricted to positive integers, but wrong on 0:

sage: A = matrix(QQbar,3,3,[[-2,-8,-12],[1,4,4],[0,0,1]])
sage: k = SR.var('k')
sage: B = A^k
sage: B
[      -2^k     -4*2^k -4*2^k - 4]
[   1/2*2^k      2*2^k      2*2^k]
[         0          0          1]
sage: [B.subs(k=i) == A^i for i in range(20)]
[False,
 True,
 True,
 True,
 True,
 True,
 True,
 True,
 True,
 True,
 True,
 True,
 True,
 True,
 True,
 True,
 True,
 True,
 True,
 True]
sage: B.subs(k=0)
[ -1  -4  -8]
[1/2   2   2]
[  0   0   1]

Change History (1)

comment:1 Changed 8 months ago by nbruin

This is not really something we can do anything about, I expect. It's just a consequence of

sage: (0^x).simplify()
0

which is wrong for x=0.

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