Questions tagged [symbolic-computation]

Numeric computation usually uses floating point numbers. Symbolic computations use symbols, and can give exact answers, such as $\sum_{n=1}^\infty \frac{1}{n^2} = \frac{\pi^2}{6}$. Mathematica, Maple, and Geometry Expressions all use symbolic computation, when desired. An online source is WolframAlpha.

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Line Integral in Octave

I want to compute Line Integral in Octave. There is a sample code that works fine in Matlab, but it does not work in Octave. ...
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Interpreting/understanding the lambertW on Maple software

I decided to use the Maple software to help me solve dynamic optimization problems, and I found this final solution for T. (example in the picture). example What does the LambertW mean for the ...
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Reduced form of symbolic expressions in sagemath

I am working in symbolic ring with two symbols: q and h. The relation between them is $q=e^h$. I want to do some algebra of matrices with symbolic entries. The entries of the input matrices consist of ...
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Are there basic techniques for proving that no elementary antiderivative exists? [duplicate]

Background: It seems there is an algorithm called the full Risch algorithm that can decide whether a given function has an antiderivative that can be expressed in terms of elementary functions. There ...
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Sympy does not recognise when two partial derivatives happen to be equal.

I am trying to find the first and second-order partial derivatives of a function of four variables $S$ using pythons symbolic math package sympy. The issue is that sympy does not automatically see ...
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Derivative of complex quadratic form-functions with respect to a vector

I have a quadratic form like this: $Q_1=v_1^TC_1(x)v_1$ $Q_2=v_2^TC_2(y)v_2$ where $x,y,z$ - $3 \times 1$-vectors $J_1,J_2,C_1,C_2$ - $3 \times 3$-matrix $v_1=x-(J_1(x)y-z),v_2=x-(J_2(y)y-z)$ ...
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Finding the symbolic expression for a particular matrix raised to the $n^{\text{th}}$ power

Consider the following matrix, with $a$ being a real number between $0$ and $1$. \text{M}=\left[ \begin{array}{cc} 1-\frac{a^2}{3} & \frac{1}{3} \left(2 a-a^2\right) \\ \frac{2 ...
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sympy: group given expressions within other expressions, e.g. $a + 2 x y + b x + 2 x z$

I would like to use sympy to locate and group instances of a given symbolic expression within a set of expressions, so that the given expression may be replaced by a variable. For instance, with ...
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I want to study the behavior of polynomials sitting in the co-ordinates of multiples of a rational point of an elliptic curve over $\mathbb{Q},$ $E(\mathbb{Q}).$ Suppose if we take a point $P = (s,t) ... 2 votes 0 answers 811 views How to use Octave with real numbers and syms at one time I want to use GNU Octave to solve my equations. Equations contain syms variables and vectors with decimal numbers in them. How properly solve these equations without getting warnings that im doing ... -1 votes 1 answer 181 views Integral of Squared Sum of Sine [closed] Let's say we have the following function $$\int \left( \sum_{i = 1}^\infty a_i \sin(b_ix)\right)^2$$ Assuming that this series converges (it is actually a Fourier Series of the Lagrangian of the Wave ... • 131 1 vote 1 answer 309 views Algorithm for expressing Gröbner basis in terms of ideal generators Given a polynomial ring and an ideal $$A \supset I = (f_1, ..., f_m)$$ there are plenty of implementations of an algorithm (e.g. Buchberger's) that produces a Gröbner basis $$G = (g_1, ..., g_n)$$ and ... • 1,044 0 votes 2 answers 87 views How to prove a transcendental equation is never zero or sometimes zero? I am an engineer by profession. Recently, while working on beams, I obtained the following transcendental equation: $$1-\cos(x)\cosh(x)+x^2\sin(x)\sinh(x)$$. I was wondering if this expression can ... 0 votes 1 answer 52 views How can you show that$(p \rightarrow q) \land (q \rightarrow r) \leftrightarrow (p \rightarrow r)$is not a tautology? Obviously,$(p \rightarrow q) \land (q \rightarrow r) \rightarrow (p \rightarrow r)$due to Hypothetical Syllogism, but how about the converse? How can I disprove the statement? 2 votes 0 answers 53 views Problem evaluating Wolfram Symbolic Integration Result ****** Note: In response to the comment below, I've modified the problem ****** I'm trying to evaluate the following indefinite integral $$\Large\int x^{-\frac{3}{2}} e^{-\frac{K}{x}\Big[(x-a)^2+(x-b)... 5 votes 2 answers 268 views Handling elementary but messy computations in proofs Often when working on a proof, I get to a computation which appears to be elementary (e.g. requiring only standard algebra and perhaps calculus) but messy. Solving this via pen and paper is tedious ... • 4,412 2 votes 1 answer 72 views Why does the function \frac{1}{x^{2222}} seem to have *two* asymptotes at around \pm0.744? When screwing around with the Dirac-delta function in Desmos i noticed that when i multiply it by a really low-degree rational function$$f(x)=\frac{1}{x^i}$$, the resulting function has the domain$$... 0 votes 3 answers 44 views How to write that the only integers that have a multiplicative inverse are$1$and$-1$, in symbolic form Could it be something like for$(1,-1) \in \mathbb{Z}$, there exists$y \in \mathbb{Z}$, such that$xy = 1$? 1 vote 0 answers 46 views what is the meaning of this element$\varphi(f|_Y)?$I have some confusion in symbolics . My confusion is given below marked in red colour what is the meaning of this element$\varphi(f|_Y)?$My main confusion about the symbolics is$(f|_Y)$? • 14.6k 1 vote 0 answers 55 views What is this hybrid symbolic-numeric algorithm for solving non-linear ODEs called? I'm an engineer so please forgive my lack of knowledge in exact mathematical terminology: For linear differential equations, it is possible to use the principle of superposition or convolution ... • 153 1 vote 1 answer 325 views Factor SYMBOLIC third degree polynomial I apology in advance for the long post... Say I have a very general 3rd-degree polynomial $$x^3 + a_1x^2 + a_2x+a_3$$ I would really like to factor that polynomial as a product of a 1st order and a ... 1 vote 2 answers 71 views Finding$b$such that$y=mx+c$is tangential to$y=b^x$. I was thinking about the following problem: Find$b$such that$y=mx+c$is tangential to$y=b^x$. My work so far: To satisfy the condition we need to find$x$such that$\frac d{dx}\left[b^x\right]=\...
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I have next task: $$\frac{\partial^2 u}{\partial x \partial y} = 0,~ u(x,x^2) = 0,~ \frac{\partial u}{\partial x}(x, x^2) = \sqrt{|x|},~|x| < 1$$ I write this, but it don't work: ...