Questions tagged [simplifying-expressions]

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

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2
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1answer
33 views

How to evaluate conditional expression for definite integral

I am trying to show that the definite integral Integrate[ (y*(1 - y) + (1 - t)*y^2 + t*(y - 1)^2)/((1 - t)*y^2 + t*(y - 1)^2)^2, {y, -Infinity, Infinity} ] is $...
2
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1answer
36 views

Identical integral evaluating differently

I am trying to compute an integral but am getting two different answers using two near-identical methods. I wish to know why they differ. ...
1
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1answer
60 views

Separating terms in an expression with many variables by their "nature"

I have an expression like this: $f=t_1(\sin(\alpha),\cos(\beta),\cos(\gamma)^2) \cdot r_1(x,y,z)+t_n(\sin(\alpha),\cos(\beta),\cos(\gamma)^2) \cdot r_n(x,y,z)$ Where $t_i$ and $r_i$ - functions of ...
1
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0answers
70 views

Checking whether the solution satisfies the equation

I want to check whether the solution f[u,v] satisfies the PDE. (As I know, all parameters are reals. So, I used Assumptions or ...
3
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3answers
142 views

How to make FullSimplify always factor out terms?

Consider the following two FullSimplify examples: a^2 q^2 + q^4 c^2 // FullSimplify q^2 (a^2 + c^2 q^2) and ...
1
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1answer
37 views

Why am I getting different results by simplifying $(a(x-b))^{m+n}(-a(x-b))^{-m-n}=(-1)^{m+n}$?

We know that $n\ge0$ and $m>0$ and both are integers. We also know that $a,b>0$. I think for any $0\le x\le b$, we should have $(a(x-b))^{m+n}(-a(x-b))^{-m-n}=(-1)^{m+n}$ But when I try to ...
1
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1answer
59 views

Re[] and Im[] yielding Arg[] [closed]

I am trying to obtain the real and imaginary parts of an eigenvalue from a matrix. ...
2
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0answers
105 views

A remarkable elimination involving the basic reproduction number R0

I have a polynomial pol of third order, whose coefficients depend on 5 parameters, and whose free coefficient is proportional to R0-1, where R0 is a certain rational function of the parameters (the ...
1
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0answers
69 views

How to solve this quintic polynomial with the solutions in its simplest final form?

Consider the following matrix: ...
-1
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2answers
62 views

Which of these expressions is greater?

With $0 \le a \le 1$, $0 \le b \le 1$, $0 \le c \le 1$, is it possible to see which of the following is greatest ...
1
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1answer
75 views

Simplifying Integrals

How can I get the expected results of 2 from this integral? ...
0
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1answer
36 views

Simplify or Solve in term of some expressions (again) [duplicate]

Suppose x=a, y=ad-bc, z=ade-bce-fga Obviously, z = (ad-bc)e-(fg)a = e(y)-fg(x) I want to get the output to be z = e(y)-fg(x) I have tried Solve[{x==a, y==ad-bc, z==ade-bce-fga},z,{a,b,c,d}] as some ...
3
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2answers
61 views

FullSimplify in term of some expressions

Is there a way to simplify some expression in term of given expressions? For example, x = a + b, y = a - b and ...
5
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2answers
129 views

How to guide Eliminate or GroebnerBasis to reduce a set of simple odes to a single ode (which can be done by Laplace Transform)

Recently, I am trying to use Eliminate or GroebnerBasis to simplify a system of ODEs. I don't want the solution of ODEs. What I ...
2
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1answer
83 views

Is possible to simplify this expression?

After I run this code: 8/Sum[(20 m + 3) (-1)^m (4 m)!/((4 Sqrt[2])^(4 m) (m!)^4), {m, 0, Infinity}] 256/(3 (32 HypergeometricPFQ[{1/4, 1/2, 3/4}, {1, 1}, -(1/4)] -...
0
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0answers
68 views

Can Mathematica simplify expressions with prescribed relations?

I have a linear map $T$ on a vector space which satisfies $T^4 = 1$ and want to simplify expressions of the form: $$[X,TY] + [Y,TX] + [Y,T[TX,TY]] + [X,T[TX,TY]],$$ where $[\cdot, \cdot]$ denotes the ...
0
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1answer
199 views

The derivation and simplification of the functions HeavisideTheta and Dirac

I encounter some problems, can you help me? Thanks. Step (1) gives the expected result 3 DiracDelta[x], why (2) and (3) can not give expected result ...
4
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1answer
68 views

Simple expansion

Why this works: TrigExpand[Sin[2 T - 2 \[Tau]cr \[Omega]cr]] while this doesn't work ...
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0answers
48 views

Simplifying commutators

Sometimes I need to simplify some commutators in the form: Doing it by hand is exhausting and boring. Does Mathematica contain a function that can handle such commutators? If not, is there another ...
0
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0answers
49 views

Use `Apply` on an expression based on its `Head`

I am making an expression into a list. Depending on the simplifications etc. using List@@ can be problematic. Eg. ...
0
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0answers
65 views

Difference between h'' and D[h[t],t,t]

In the output of the following code block, simplification of h''[t] produces the same result as D[h[t],t,t]. But the form produced by h''[t] has a removable singularity that causes trouble (division ...
5
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1answer
227 views

Does Mathematica simplify calculation when encounter zero?

e.g. when Mathematica Calculating f[x0]=A[x0] B[x0], where A[x] & B[x] could be some complicated high dimensional function. Will Mathematica outcome 0 directly ...
1
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3answers
129 views

How can I teach Mathematica to break divergent integrals into terms?

For instance, I get the following expression: $\int_0^{\infty } \left(\frac{e^2 x}{e^{2 x+2}-e^{2 x}}-\frac{x}{e^{2 x+2}-e^{2 x}}-\frac{e^2}{2 \left(e^{2 x+2}-e^{2 x}\right)}+\frac{3}{2 \left(e^{2 x+2}...
1
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2answers
88 views

Symbolic Matrix/Operator Multiplication in Mathematica

Let A,Band C be three 4x4 matrices defined as A=x*P+y*Q-R...
4
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1answer
148 views

Evaluation of formula reduces domain and FullSimplify is wrong

I would like a closed form for the formula Sum[Binomial[k - b, n] Binomial[n + b, a], {n, 0, k}] where variables k, a, b are ...
0
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0answers
69 views

Fully expanding and distributing a symbolic sum

I have quite a large expression I want to simplify. For example, this can be generated by a recursive definition: ...
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0answers
79 views

Use self-defined operator symbol simplify formula

Mathematica is very useful and powerful in symbol compute, but some output isn’t concise if we didn’t simplify. Can i predefined some operator? eg. Lie bracket. Here is a minimum example. Suppose ...
3
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3answers
114 views

Simplify expression by a known expression substitution

A bit complex than a similar question, below is a minimal example, eqs1 = a b x'[t]^2 - ac x''[t] eqs2 = x''[t] - b x'[t] - c == 0 I want take ...
0
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1answer
84 views

Simplifying multiplies of sums into a single double sum

I have the following expression: Sum[x^n, {n, 1, Infinity}]*Sum[Log[m, x], {m, 2, Infinity}] How can I Force Mathematica to write this expression in the following ...
0
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1answer
34 views

Simplifying an equation in which all the terms are integrals with respect to the same variable

I have an equation in the following form: Integrate[A[x], x] + Integrate[B[x], x] == Integrate[C[x],x] How can I simplify this equation to get: ...
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0answers
34 views

Simplify including dim of matrix as parameter

I want to check that an identity about matrix is true for all dim n. My idea is to view dim n as a parameter and then Simplify the expression. For example,I hope <...
0
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0answers
41 views

Substituting a two term expression with two rule on one variable with which each of the rules simplify one of the terms

I have two expressions as follows: r (Sin[t]+Cos[t]) and the rules for simplification are: {x == b + x Cos[t], y == r Sin[t]} ...
2
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2answers
192 views

How to express Bessel Functions in terms of Hankel Functions

I have the following expression BesselJ[\[ImaginaryI]*m, k*r] FunctionExpand knows how to transform from ...
1
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2answers
48 views

Rearrange the parts of formula expression

Below is a minimal example, D[k[θ[t]]*θ[t] == θ'[t], t] // TraditionalForm Output is $$ \theta (t) \theta '(t) k'(\theta (t))+k(\theta (t)) \theta '(t)=\theta ''(t)...
2
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2answers
55 views

Compare the coefficient in same part of the equations

I want to use Mathematica to do certain calculations. Below is a minimal example, my goal is to solve the equations that result from comparing the coefficients of both polynomials ...
0
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1answer
61 views

Forcing mathematica not to substitute some terms in an expression

I have an expression c which should be defined before the function and a function f defined as follows: ...
0
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4answers
46 views

Simplifying an equation by factoring the current coefficients in order to substitute a new coefficients

I have an equation in the following form: a*x + b*y + c*z == d I want to substitute the following constants instead of a,b,c,d: ...
1
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3answers
67 views

How to help Eliminate simplify simultaneous equations

I have a set of three moderately simple simultaneous equations that I'd like to simplify and eliminate a set of variables for (this is a simple example of a more general class of problem - but I'd ...
3
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1answer
219 views

How to simplify only one side of an equality?

Suppose we have two expressions and == between them. I want to simplify only the right-hand side. What should I do?
0
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0answers
52 views

How to evaluate simplify an expression containing derivatives

I have an expression that is a derivative of order 2. I want to assign value to derivatives of orders lower than 2(e.g. the expression itself) which should cause the derivatives of higher order become ...
0
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0answers
33 views

How to simplify half integer gamma functions using ComplexityFunction?

There's a similar question already: Replacing gamma at half integers by double factorial But I wanted to be able to simplify expressions like the following using ComplexityFunction. Equation Source ...
0
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0answers
36 views

How to find all the tree leaves of an expression?

I'd like to better understand what mathematica is doing during simplification, so I tried expression //TreeForm //TreeLeaves to see what it's picking up on. Except ...
4
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1answer
90 views

Cos[sqrt[-x]] == Cosh[sqrt[x]] but not Cos[sqrt[-(x+y)]] == Cosh[sqrt[(x+y)]]?

I have trouble with the following apparent contradiction: ...
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0answers
38 views

Simplifying the following expression?

Continuing from this question: How do I simplify the equilibrium point to this simplified expression? We found our equilibrium points. We also define $$\mathcal{R}_0= \frac{[\beta_1 b_3(\epsilon p+b_1(...
1
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1answer
37 views

Simplify function with condition not working [duplicate]

I try to simplify the function Q below: Q[x_] := Sign[x] /; x > 1 Simplify[Q[x], Assumptions -> x > 1] (*return Q[x]*) But it doesn't work. However, if I ...
2
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2answers
218 views

How do I simplify the equilibrium point to this simplified expression?

Install the following package: ...
0
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1answer
44 views

How to remove Wrong relations after LogicalExpand?

I have a complex relation which I need to expand and represnt it clear and nice. So I used LogicalExpand (LE). I know LE does only the simple expansion and nothing further. but it creates some wrong ...
0
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0answers
33 views

Simplify expression with assumption that all variables are real

I have an expression in which all variables are real. However when I simplify the expression with appropriate assumptions a 'Conjugate' still remains. How can I get rid of this? Here is my code ...
1
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1answer
55 views

Why do these results differ?

...
1
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1answer
62 views

How can I simplify these formulas?

I got these formulas from computation: ...

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