I try to include sympy in teaching material.
When doing this, the focus is not on programming nor implementation
details. The CAS should be as "transparent" as possible. The CAS-using
code should read like the math done in a textbook.
I think sympy is very close to this. However, there are some annoying
obstacles to transparency.
One of it is the return behavior of solve. There are at least three
cases (if a solution can be found):
* a dict
* a list of tuples
* a list of dicts
for me it is hard to predict, when which case will occur. The behavior
can be influenced by keyword args but this would require additional
(off-topic) explanation to the students..
So, I am thinking in implementing my own wrapper for solve to overcome
this. However, I from my point of view it would be a lot cleaner if the
default return type (in the case of a unique solution) is always one
dict. Because then the solution can immediatly passed to subs(...).
Question: Is there any chance to change the solve behavior like that? (I
would try to work on it.)
See an example of what I mean (copied from an IP notebook):
In [1]:
import sympy as sp
print sp.__version__
0.7.5
In [2]:
x1, x2 = xx = sp.Matrix( sp.symbols("x1:3") )
z1, z2 = zz = sp.Matrix( sp.symbols("z1:3") )
In [3]:
q = sp.Matrix([x1, -x2 + x1*(1-x1**2)])
q
Out[3]:
Matrix([
[ x1],
[x1*(-x1**2 + 1) - x2]])
Say z:=q(x). We want to calculate x=q^{−1}(z). We use 0=z−q(x) as
expression to solve.
In [4]:
sp.solve(q-zz, xx) # returns a list (len=1) of tuples (len=2) of
expressions
Out[4]:
[(z1, -z1**3 + z1 - z2)]
In [5]:
# This is what I finally want to do:
# q_inv = xx.subs(x_sol)
# but this requires some overhead
sp.solve(q-zz, xx, dict=True) # returns a list (len=1) of dicts
Out[5]:
[{x1: z1, x2: -z1**3 + z1 - z2}]
In [6]:
x_sol = sp.solve(q-zz, xx, dict=True)[0]
q_inv = xx.subs(x_sol)
q_inv # this is the result I want (but with less 'magic' overhead)
Out[6]:
Matrix([
[ z1],
[-z1**3 + z1 - z2]])
In [7]:
# on the other hand, solve can behave like 'expected' (by me):
sp.solve(q-zz, zz) # returns one dict (good)
Out[7]:
{z2: -x1**3 + x1 - x2, z1: x1}
Best regards,
Carsten.
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