# Tagged Questions

Questions on manipulating complicated expressions and making them look simpler using Simplify, FullSimplify and Reduce.

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### Why is result from evaluation not simpler? [on hold]

How do I define variables $\qquad u(x_m , y_n)\qquad m,n=1,2,\dots,4$ in Mathematica? $x_m, y_n$ are known and $u$ is unknown. The result I am getting is: ...
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### Substutution of Ansatz of an ODE [duplicate]

I am only beginning to learn to use Mathematica, and got stuck while trying to implement what is apparently a simple substitution rule. So I have a second order ODE in f, and I want to put in the ...
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### Simplify a complex trigonometric equation resulting from constraint solving

In the solving of mechanical constraints, I often meet complex trigonometric equation that I have to simplify. Here the equation I would like to simplify : Mathematica notebook presenting the ...
101 views

### How to tell Mathematica to avoid simplification of product of exponentials with the same base?

There has been a similar question, but it doesn't solve my problem. I have this input: var = Exp[a] Exp[b] And the output is ...
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### Replacing expressions with variables [closed]

I have a large matrix where the entries are rational in Jacobi elliptic functions e.g. I'd like to replace the elliptic functions by variables, e.g. ...
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### Efficient method to calculate green's function between points

I am working on an analytical model for sound radiation from a cylinder. As part of this work I am using the boundary element method to predict the sound pressure at a particular location away from a ...
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### Trouble factoring an expression

I've got the term $-1 + 2b^2 + 2b\sqrt {b^2-1}$ appearing several times within several larger expressions. It is easy to see that this expression factors into ${(b+\sqrt{b^2-1})^2}$, but when I use <...
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### Simplification of Gamma functions

I am having some trouble simplifying some Gamma functions. I have a large expression in which some combinations of Gamma functions appear, that can be simplified, but applying ...
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### Verifying inequality in Mathematica

I am trying to verify the following inequality Mathematica. This I wrote the fillowing code: ...
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### Factor a polynomial Root into Roots of smallest possible degree

Suppose I have a polynomial Root representing an algebraic number. I want to represent it (if possible) as a product of several polynomial ...
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### Simplifying polynomials with conditions on variables

I'm working with polynomials of 5 variables $a,b,p,q,r$ which have a condition $a+b=p+q+r$. I'd like to minimize the number of variables in the answer. However, FullSimplify can't handle even simple ...
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### Simplify sum of complex logs to single real log

Sometimes, mathematica likes to give me complex results when, e.g, integrating a real valued function. The result might be something like ...
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### Collect partial derivatives and rewrite them with delta/nabla

Ultimately, I wish to get the higher generalized product rule for Laplacian. That is, we have $\Delta(fg)=f\Delta g+2\nabla f\cdot\nabla g+g\Delta f$ but what is $\Delta^n(fg)$? I am tying to guess ...
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### Expectation of summation with symbolic indices

I am working on symbolic computations with mathematica. I faced an issue with taking expectation of a large expression involving summations with symbolic indices. Is it possible to take expectation ...
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### Simplify results further

I have an extremely long result in polynomial form following some matrix operations. However, given the symmetry of the problem, I can safely say that the solution will reduce much further than is ...
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### difference between FullSimplify and Simplify

I have a problem to dinstinguish the following two mathematica codes, the only difference is the first use FullSimplify and the second is Simplify. but the results are totally different. what is wrong,...
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### Simplifying x Conjugate[x]

I am trying to simplify a big expression containing many times terms of the form x Conjugate[x]. While this works for a single term: ...
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### Complicated implicit plotting [closed]

I'm quite new to Mathematica and have already spent tons of time on problems of this type, browsing through tutorials and topics here. I'm now coming to conclusion that it cannot be done and am about ...
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### Simplify: Why does it miss this simple one?

I got a result with the expression ...
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### Simplifying integer inequalities to equality

I try (in Mathematica 10) FullSimplify[l >= l1 + l2, {l <= l1 + l2, Element[l | l1 | l2, Integers]}] But that gives back ...
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### Symbolically prove that two expressions are identical

I encountered this problem when trying to reproduce the result of this paper. (The relevant parts are all included in the preview i.e. the 1st page of the article. This link is just given as ...
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### Metric Simplify & grouping

I'm changing a basis from one metric to another. When simplifying the result Mathematica doesn't seem to grasp all the possible simplification: ...
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### Problem with simplification of $\sqrt{1+\frac{y^2}{x^2}}$

When I evaluate my Mathematica code I get out a term of the following form: $\sqrt{1+\frac{y^2}{x^2}}$. However, I also have $\sqrt{x^2+y^2}$ terms that I would like it to cancel with. For example, ...
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I have the following inequality to solve for $R$ in terms of $\delta$ and $n$, with assumption that $n \geq 3$ and $\delta>0$: $$-2 < 2 -\frac{16n\delta^{2}}{R^{2}\sin^{2}\frac{\pi}{n}} \left(... 1answer 242 views ### Simplifying square root of exponential Very simple question: Why doesn't Mathematica simplify this square root expression? Refine[Sqrt[Exp[I p]], p > 0] // FullSimplify It should give ... 1answer 27 views ### Making multi-linear polynomial change of variables (simplifications) by updating replacementFunction This is an evolution of one of my previous questions; I've got a partial answer to that question and now have a much cleaner question to ask: Question: What changes to ... 3answers 220 views ### Why doesn't Lambert function (ProductLog) simplify? I have Simplify[ProductLog[x*Exp[x]]] By the definition of the Lambert function, this should be simply x. But Mathematica outputs this: ... 0answers 145 views ### Problem of calculating the residue of a expression (to confirm the result from a paper) [duplicate] I use Mathematica to confirm a result from a paper which is to calculate the residue of a expression at zero. The code and result are given below. Is this residue too complicated for Matheamtia or ... 1answer 135 views ### Residue failed to reproduce this residue in a paper This problem is a more clearly state of my original problem which is off topic, so I reconsider my problem carefully based on previous discussions, and gives the following valid code to reproduce my ... 0answers 48 views ### NCAlgebra: define a scalar variable I have a linear operator L and a scalar h, and would like to expand L[f + h phi] to ... 1answer 74 views ### Replacing patterns (determinants) in a rational multivariate function and/or getting replacementFunction to work on a multi-linear expression Given a rational multivariate function known to contain determinants, what is the best way to rewrite the function in terms of the determinants? A simple example: ... 2answers 110 views ### Factor out imaginary unit of root of obviously negative term Suppose I have the term t=\sqrt{-a^2-b^2}, where a,b\in\mathbb R. Of course, we know that it holds$$ t = \mathbb i \sqrt{a^2+b^2} $$which is (in my opinion) more convenient. How can I get ... 1answer 87 views ### A simplification of a complex expression I use mathematica to confirm a result from a paper ("... 2answers 87 views ### Checking inequalities: How can x>0,y>0 yet x+y indeterminate? I have the following: ... 0answers 39 views ### Evaluating a function after simplifying to avoid infinite expressions My Poly[j_, s_] function simplifies to a polynomial for all j. So I defined a PolySim[j_, s_] = Simplify[Poly[j,s]] function. However, if I try to evaluate PolySim[j,0], since this is PolySim[j,0] = ... 0answers 80 views ### Bringing rational functions to canonical form I have a complicated expression, which among other things has stuff like functions of rational functions: expr = f[x/(-x^2 + y)] + f[-(x/(x^2 - y))] (* + ...*) ... 0answers 66 views ### Avoiding divide by zero to simplify an expression enough to solve I have a very complicated expression that I'm trying to set to zero and solve. I simplify by substituting in variables, but Mathematica isn't fully simplifying it -- my guess is because it thinks it ... 0answers 79 views ### Why isn't Mathematica listening to my assumptions? I'm trying to simplify the expression ωplus := 1/2 c (I f V + Sqrt[4 k^2 - f (f + 8 I k) V^2]) so that I can get it in the form a+i b. I am using the global ... 1answer 64 views ### Need help on simplifying the integral of a square root of a polynomial I have the following expression a = 4 Cos[af / 2]^2; b = 1 - 5 Cos[af / 2]^2; c = Cos[af / 2]^2; s = Sqrt[a*x^4 + b*x^2 + c] and I need the integration of s in ... 1answer 79 views ### Weird behavior of HypergeometricPFQ Consider the following function: fun = HypergeometricPFQ[{1, x1-y1, 1-x1-y1-2u}, {x2-y1, 3-x2-y1-2u}, 1]; Let us try and evaluate this function on the following ... 1answer 521 views ### RootSum result manipulation/simplification Consider the sum sum1 = Sum[ k/( k^7 - 2 k + 3), {k, Infinity}] ... 2answers 71 views ### Simplifying expressions containing unit of zero magnitude I have obtained the following form as a part of a computation: k (Quantity[0, "Kilohertz"]) + Quantity[1/500, "Kilohertz"] This is typeset as Here, ... 0answers 33 views ### Mathematica can't simplify disguised expression [duplicate] When I simplify the following quartic polynomial with a linear constraint; Simplify[x y z a + x y z b , a + b + c == 0] // Expand I get what to me seems like the ... 1answer 86 views ### Way to simplify an inequality with many variables my problem is the following: I have three inequalities in five variables x,u,a,b,c\in \mathbb{R},x>0 : ... 1answer 105 views ### Adding irrelevant assumptions changes the result of Simplify I've run into this problem a number of times. A typical example is Simplify[Sign[k], {0 < A, 0 < B, A*Exp[2*y] < k, y > 1}] which evaluates to 1, ... 0answers 44 views ### QPochhammer function simplification? Consider the function which in Mathematica is denoted as QPochhammer[a,q,n], and its infinite product cousine: which in Mathematica reads ... 4answers 417 views ### Mathematica not able to confirm its own solution to differential equation I type the following into Mathematica: DSolve[q''[x] + 2 x/(x^2 - 1) q'[x] - 4*q[x]/(x^2 - 1) == 0, q[x], x] It gives me the result ... 2answers 126 views ### Simplifying ArcTan[Cos[u], Sin[u]] I am trying to evaluate the following expression in Mathematica:$$ \bigg| \frac{\left(1-z^{-2}\right)^n}{\left(1-z^{-1}\right) \left(2-z^{-n}-z^{-1}\right)} \bigg|^2  Here $z$ is the complex ...
I have set of recursive function definitions and assumptions $\forall n.t1(n+1)=t1(n)-Y*S(n)$ $\forall n.t2(n+1)=t2(n)+S(n)$ and assumption $\forall n.n<K\rightarrow L1=L2*t2(n)+t1(n)$ I want ...