Opened 3 years ago
Last modified 3 years ago
#20755 new defect
Bug in solve due to a bug in symbolic_expression_from_maxima_string
Reported by: | bruno | Owned by: | |
---|---|---|---|
Priority: | major | Milestone: | sage-7.3 |
Component: | symbolics | Keywords: | maxima, solve |
Cc: | Merged in: | ||
Authors: | Reviewers: | ||
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description
A bug in sage.calculus.calculus.symbolic_expression_from_maxima_string
implies bugs in solve
and roots
for symbolic expressions.
Symptoms
The method solve
for symbolic expressions is buggy (the list of multiplicities has size 2 instead of 4), as well as roots
as a (serious!) consequence:
sage: w = x^4 - (1+3*i)*x^3 - (2-4*i)*x^2 + (6-2*i)*x - 4 - 4*i sage: w.solve(x,multiplicities=True) ([x == -1/2*sqrt(2*I) + 3/2*I - 1/2, x == 1/2*sqrt(2*I) + 3/2*I - 1/2, x == (-I + 1), x == (I + 1)], [1, 1]) sage: w.roots() # should be 4 roots [(-1/2*sqrt(2*I) + 3/2*I - 1/2, 1), (1/2*sqrt(2*I) + 3/2*I - 1/2, 1)]
Diagnosis
- The behavior of
roots
is easily explained by the behavior ofsolve
, sinceroots
assume that the length of the list of solutions is the same as the length of the list of multiplicities. This should clearly be the case so the bug is not inroots
.
- Given the parameter in the example,
solve
calls Maxima and parses the result. The multiplicities are obtained by invokingP.get('multiplicities')
. This is the right invocation to Maxima, no bug there.
- To parse the solutions returned by Maxima,
solve
callssage.symbolic.relation.string_to_list_of_solutions
, which itself callssage.calculus.symbolic_expression_from_maxima_string
. The bug occurs in this last function: Indeed, while there is no apparent reason for this, invoking this function changes the variablemultiplicities
of Maxima. Here is an example:
sage: w = x^4 - (1+3*i)*x^3 - (2-4*i)*x^2 + (6-2*i)*x - 4 - 4*i sage: m = (w == 0)._maxima_() sage: P = m.parent() sage: s = m.solve(x).str() sage: s # the list of solutions returned by Maxima '[_SAGE_VAR_x=-(sqrt(2*%i)-3*%i+1)/2,_SAGE_VAR_x=(sqrt(2*%i)+3*%i-1)/2,_SAGE_VAR_x=1-%i,_SAGE_VAR_x=%i+1]' sage: P.get('multiplicities') # correct! '[1,1,1,1]' sage: l = sage.calculus.calculus.symbolic_expression_from_maxima_string(s) sage: l [x == -1/2*sqrt(2*I) + 3/2*I - 1/2, x == 1/2*sqrt(2*I) + 3/2*I - 1/2, x == (-I + 1), x == (I + 1)] sage: P.get('multiplicities') # WTF??? '[1,1]'
Change History (2)
comment:1 Changed 3 years ago by
- Type changed from PLEASE CHANGE to defect
comment:2 Changed 3 years ago by
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Well,
multiplicities
is a system variable. See http://maxima.sourceforge.net/docs/manual/maxima_20.html. Who knows when it gets updated? In particular, the reconstruction of symbolic expressions from strings might be calling into maxima again.The quick fix is to get the correct value of
multiplicities
out as soon as we can, before conversion back.In the longer run, it would be preferable to do the conversion while avoiding strings altogether. See
sr_sum
andsr_limit
etc. for examples how one can usesr_to_max
andmax_to_sr
to convert.