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Questions tagged [symbolic]

For questions about symbolic computation, as opposed to numerical computations.

For questions about symbolic computation, as opposed to numerical computations. Because of its capabilities in symbolic computation, Mathematica is often considered to be a Computer Algebra System (CAS).

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1573 questions
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Non-commutative algebra

I'm constantly dealing with non-commutative algebras. ** is inbuilt, non-commutative and associative. That's good :-) But it is not distributive. Rats. What is a simple way (I probably won't need much more) to have, say, (a1 + a2 +…
Hauke Reddmann
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Symbolic computations with already assigned variables

For example I have assigned some variables that could defined in terms of each other. Then I for some reason need to derive some formula using this variables. How to show the result of this computation without substituting the values and how then…
swish
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Use both values of $\pm$ in equations

Is there an elegant way to use $\pm$ in equations, without having to make a text change and substitution using an Or function? For instance, I would like this equation Solve[x \[PlusMinus] 2 == 0, x] to be solved to {{x -> -2},{x -> 2}} and…
David G. Stork
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How to symbolically differentiate an infinite series without evaluating the series itself

I'm dealing with finite sums of infinite series. Each of the infinite series possesses a different starting index, i.e. each of the series begins at n = 0, n = 1, or n = 2. As a result, it's important to keep track of the indices for each of the…
Rob
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Symbolic manipulation with unevaluated sums

If I have two expressions with sums in them, like this: $$\begin{align*} b&=\frac{\sum_{i} (x_i - \bar{x})(y_i -\bar{y})}{\sum_{i}(x_i -\bar{x})^2}\\ r&=\frac{\sum_{i} (x_i - \bar{x})(y_i -\bar{y})}{\sqrt{\sum_{i}(x_i -\bar{x})^2\sum_{i}(y_i…
Mr Alpha
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Wallis Formula and Pippenger Product---How do we get symbolic output?

The Wallis Formula computes $\frac{\pi}{2}$ OEIS and the Pippenger Product computes $\frac{e}{2}$ OEIS. Here is a combined formula: x = 0; (*Wallis Formula (Pi/2)*) Defer[ 2^(1/2^x) Product[(1 - (2^j + 2 k + 1)^-2)^(2^x)^(-j - 1), {j,1,…
Fred Daniel Kline
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Laplace transform of a rectangle function

I defined a rectangle function as below: rect[t_, T_] := (Sign[t] - Sign[t - T])/2 The laplace transform should be $$ \frac{1-e^{-sT}}{s} $$ But the code below in Mathematica won't work: LaplaceTransform[rect[t, T], t, s] // Simplify It just throw…
diverger
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Comparison of Dispatch objects ureliable in Mathematica 10

In 2008 I wrote a group theory package. I've recently started using it again, and I found that one (at least) of my functions is broken in Mathematica 10. The problem is complicated to describe, but the essence of it occurs in this line: l =…
Leon Avery
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Factorising blinear forms with Mathematica

Say I have some symbolic output that looks like the following: expr = A a1 b1 + B a1 b2 + C a2 b1 + D a2 b2 I would like to factorise this in the following way: Input: FactorQuadratic[expr, {a1, a2}, {b1, b2}] Output: { { A, B }, { C, D } } In such…
catalogue_number
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Solving symbolic equation for fraction of variables

Suppose there is an equation like this (overly simplified example): eqn1 = ui - ua r1 / (r1 + r2) == 0 How can I get Mathematica to "solve" the equation in terms of: eqn2 = v == ua / ui i.e. have Mathematica deliver v == 1 + r2 / r1 as a…
Robert GID S.
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Using Resolve and ForAll to prove takes a really long time

I've been trying to prove a lemma for my paper using Mathematica... basically that $$\forall \{n, d_i, d_j\} \in \mathbb{Z},\ n \ge d_i > d_j \ge 2$$ it's true that $$V[1, n, d_i-1, d_j-1] > 0 \Longrightarrow V[1, n, d_i, d_j] > 0$$ When I…
Art
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What is the operator for inverting the sign of the argument of a function?

I want an operator that takes as input a function of a real variable e.g. f(x) and returns as output the answer f(-x). How does one define such an operator in Mathematica?
Quasar Supernova
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What's the differences between the shift-enter and MakeBoxes running?

I know the example usages of MakeBoxes in the Tutorial like this. but I want to know a subtle distinction between (1) and (3) gplus /: MakeBoxes[gplus[x_, y_, n_], StandardForm] := RowBox[{MakeBoxes[x, StandardForm], …
Junho Lee
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What is so special about variable s$?

I found a nice bug in Mathematica 9.0.1.0. Could anyone check to reproduce it? Create a file temp.txt with one line: Attributes[s$] = {Temporary} Load it into Mathematica with <<. Now calculate: Sum[x^(-n)*y^n, {n, 0, Infinity}] Mathematica…
Vlad
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Illogical failures of symbolic integration over Boole

Is there a way to work around integration over Boole being mysteriously flaky like examples show below? Is there a meaningful explanation for this behaviour? First, rather obvious integral stays unevaluated: Integrate[Boole[u^2 + v^2 < 1], {u,-1,1},…
kirma
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