Don't feel stupid, but learn from your mistakes. Go beyond "this works / this doesn't work":
> [c[i] for i in range(0..2)] <-- this doesn't work Read error messages, they contain useful information. ``` sage: [c[i] for i in range(0..2)] --------------------------------------------------------------------------- TypeError Traceback (most recent call last) <ipython-input-...> in <module> ----> 1 [c[i] for i in range(ellipsis_iter(Integer(0),Ellipsis,Integer(2)))] TypeError: 'generator' object cannot be interpreted as an integer ``` Here, you can see that - `range(0..2)` was preparsed as `range(ellipsis_iter(Integer(0),Ellipsis,Integer(2)))`, - we get a type error because something (here: range) expected an integer and got something else This gives a clue of what went wrong: range wants integer arguments: range(2), range(1, 3); but not range of an ellipsis iteration like `0 .. 2`. Now, about the proposed code after fixing this range mistake. After defining: ``` sage: R = PolynomialRing(RR, 'c', 20) sage: c = R.gens() sage: c = vector([c[i] for i in (0 .. 2)]) sage: Z1 = matrix([[1, 2], [3, 4]])*vector([c[1], c[2]]) ``` we have: ``` sage: Z1 (c1 + 2.00000000000000*c2, 3.00000000000000*c1 + 4.00000000000000*c2) sage: Z1[0] c1 + 2.00000000000000*c2 ``` This `Z1[0]` is a polynomial, not a symbolic expression: ``` sage: parent(Z1[0]) Multivariate Polynomial Ring in c0, c1, c2, ..., c18, c19 over Real Field with 53 bits of precision ``` So `== 0` tests whether it is zero: ``` sage: Z1[0] == 0 False ``` and does not give a symbolic equation. To get an equation, convert `Z1[0]` to the symbolic ring: ``` sage: SR(Z1[0]) == 0 1.00000000000000*c1 + 2.00000000000000*c2 == 0 ``` To use `solve`, both the equation and the variable must be in the symbolic ring. Converting polynomial variables over the floating-point reals `RR` to symbolic variables is a little more tricky: ``` sage: SR(c[1]) 1.00000000000000*c1 sage: SR(c[1]).variables()[0] c1 ``` >From there: ``` sage: solve(SR(Z1[0]) == 0, SR(c[1]).variables()[0]) [c1 == -2*c2] ``` Working over the integers or the rationals simplifies things a bit: ``` sage: R = PolynomialRing(QQ, 'c', 20) sage: c = vector(R.gens()) sage: c[1:3] (c1, c2) sage: Z1 = matrix([[1, 2], [3, 4]])*c[1:3] sage: Z1 (c1 + 2*c2, 3*c1 + 4*c2) sage: Z1[0] c1 + 2*c2 sage: SR(Z1[0]) c1 + 2*c2 sage: SR(c[1]) c1 sage: solve(SR(Z1[0]) == 0, SR(c[1])) [c1 == -2*c2] ``` Note that for equations of the form `== 0`, you can skip the `== 0` when calling `solve`, feeding it only the left hand side: ``` sage: solve(SR(Z1[0]), SR(c[1])) [c1 == -2*c2] ``` -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-support/ef4c405c-7160-41fa-96c0-522fcde7cfa4n%40googlegroups.com.
