ASKSAGE: Sage Q&A Forum - Latest question feedhttp://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Tue, 22 Oct 2019 07:25:00 -0500Functions order truncation (linearization)http://ask.sagemath.org/question/48465/functions-order-truncation-linearization/ I want from from expression like
$$e = (1 + h + \frac{\partial h}{\partial x}) (1 + h + \frac{\partial h}{\partial y})$$
arrive to
$$e \approx 1 + 2h + \frac{\partial h}{\partial x} + \frac{\partial h}{\partial y} + O(\dots)$$
by assumptions $h \ll 1; \frac{\partial h}{\partial x} \ll 1; \frac{\partial h}{\partial y} \ll 1$
Is there instrument for such transformations in sagemath? The problem I'm running into is $h$ being function of some vairables, while every occurance of big O notation in documentation operates on some ring variable.versusvoidTue, 22 Oct 2019 07:25:00 -0500http://ask.sagemath.org/question/48465/Substitution of multiple variables, for linearizationhttp://ask.sagemath.org/question/42822/substitution-of-multiple-variables-for-linearization/ Hi
we want to substitute multiple variables, for example
x1*x3 would be z1, x2*x4 would be z2 and so on.
We save all combinations of monomials in a dictionary, then we wanted to use subs to replace the variables, but it does not work.
How could one implement this?
The purpose is for linearization of a large system of equations.
A system like this:
x[1] + x[1]*x[2]*x[3] + x[1]*x[4]*x[6] + x[1] + x[4] + x[5] + x[7],
x[0]*x[1]*x[4] + x[0]*x[1] + x[2]*x[4] + x[3]*x[5]*x[6] + x[3]*x[5] + x[7] + 1,
x[1]*x[2] + x[2]*x[3]*x[6] + x[2]*x[4] + 1,
x[0]*x[5]*x[6]*x[7] + x[1]*x[7] + x[2] + x[7],
x[1]*x[3]*x[7] + x[4] + x[5]*x[6] + x[6],
x[1]*x[3] + x[2]*x[4] + x[3]*x[4]cryptoWed, 04 Jul 2018 04:11:49 -0500http://ask.sagemath.org/question/42822/