Questions tagged [simplifying-expressions]
Questions on manipulating complicated expressions and making them look simpler using Simplify, FullSimplify and Reduce.
2,083
questions
2
votes
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
votes
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
vote
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
vote
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
votes
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
vote
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
vote
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
votes
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
vote
0answers
69 views
How to solve this quintic polynomial with the solutions in its simplest final form?
Consider the following matrix:
...
-1
votes
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
vote
1answer
75 views
0
votes
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
votes
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
votes
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
votes
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
votes
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
votes
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
votes
1answer
68 views
Simple expansion
Why this works:
TrigExpand[Sin[2 T - 2 \[Tau]cr \[Omega]cr]]
while this doesn't work
...
0
votes
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
votes
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
votes
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
votes
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
vote
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
vote
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
votes
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
votes
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:
...
1
vote
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
votes
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
votes
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
votes
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:
...
0
votes
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
votes
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
votes
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
vote
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
votes
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
votes
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
votes
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
vote
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
votes
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
votes
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
votes
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
votes
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
votes
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:
...
1
vote
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
vote
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
votes
2answers
218 views
How do I simplify the equilibrium point to this simplified expression?
Install the following package:
...
0
votes
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
votes
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
vote
1answer
55 views
1
vote
1answer
62 views
