Questions tagged [assumptions]
Questions about the function Assuming[], the $Assumptions system variable, and the Assumptions option of functions such as Simplify[] and Integrate[].
411
questions
8
votes
1answer
108 views
Why does Simplify work diferently for (a+b)/e versus (a+b+c)/e?
I am playing around with Simplify amd assumptions. I noticed that:
Simplify[x > (a + b)/e, x < (a + b)/e]
...
1
vote
1answer
47 views
How to evaluate a multidimensional NIntegral in a range where certain conditions must be satisfied by the variables
I have a function f which looks similar to this :
f[a_, b_, c_] := NIntegrate[sigma[a, b, c], {a, -valueA, valueA}, {b, -valueB, valueB}, {c, -valueC, valueC}]
and ...
2
votes
1answer
66 views
0
votes
1answer
52 views
Specifying assumptions at the start of a piece of code
I am aware of the use of 'Assumptions' or 'Assuming' to attach to certain operations (e.g. integrals) to aid Mathematica. Is there a way of listing asssumptions at the beginning of a piece of code ...
0
votes
1answer
47 views
How do I introduce an assumption when defining a piecewise function?
Define m as an integer. I want to specify a Piecewise function f[x,n] that takes value ...
3
votes
1answer
60 views
NMinimize with assumptions gives result that does not satisfy assumptions
I am trying to determine if a function is always positive given a set of assumptions. I am using NMinimize following the advice of previous posts in this site. ...
0
votes
0answers
39 views
Regarding “Assumptions” under “Integrate”
Sir,
I tried to integrate the following in mathematica
...
0
votes
1answer
36 views
Need help understanding the results of the unit function
I want to get Limit of the following function at $T\to 0$.
$$
Eig=\frac{8 (\eta +J \sinh (2 \beta \eta ) \sinh (2 \beta J)+\eta \cosh (2 \beta \eta ) \cosh (2 \beta J))}{\eta Z^2}
$$
where $Z=2 (...
3
votes
1answer
69 views
Solve an equation with real parameters
I am trying to solve
$$
\left(\eta ^2-1\right) \cosh ^2(\beta \eta )+2 J^2=2 \eta (J \sinh (\beta \eta ) \sinh (\beta J)+\eta \cosh (\beta \eta ) \cosh (\beta J))
$$
for $\eta$. Where, $\beta, ...
0
votes
1answer
54 views
Problem with DiracDelta evaluating to zero
I am having an issue (in Mathematica 11.2.0.0) where the following integral evaluates to zero:
...
0
votes
1answer
44 views
How can I add assumptions on the coefficients when using FindFit? [closed]
I have an equation of the following type:
$$f(z) \overset{!}{=} a f_a(z) + \sum_{s=0}^\infty c(s) f_c(z,s)\tag{1}$$
where I know $f$ numerically and $f_a$ and $f_c$ analytically (they are long, ...
0
votes
0answers
30 views
Truncate series with real powers that are not fully numerical
Take a function with the following expansion
A3[z_]:=Sum[Subscript[a3x, jj]*z^jj, {jj, 0, 2}] + z^r Sum[Subscript[a3NAx, jj]*z^jj, {jj, 0, 1}];
where ...
0
votes
0answers
96 views
Rubi/Mathematica gives different values for the same integrand
Consider this integral:
$$
\int_0^\pi d\theta \sin\theta\, {1 \over \gamma^q}\left((1-\gamma^2)^2\sqrt{1 \over 1-\left(1-(1-\gamma^2)^4\right)\cos^2\theta} - 1\right)^q
$$
for $0\leq \gamma < 1$. ...
1
vote
1answer
71 views
complex number from the integration of a real integrand
Consider this integral:
$$
\int_0^\pi d\theta \sin\theta\, {1 \over \gamma^q}\left((1-\gamma^2)^2\sqrt{1 \over 1-\left(1-(1-\gamma^2)^4\right)\cos^2\theta} - 1\right)^q
$$
for $0\leq \gamma < 1$. ...
1
vote
1answer
63 views
Two different Integration results for the same integrand in Mathematica
I want to calculate
$$
\int_0^\pi d\theta\sin\theta\, \left(\sqrt{1 \over 1-\left(1-(1-\gamma^2)^4\right)\cos^2\theta} - 1\right)^q
$$.
For the simplest case of $q=1$ we have
...
2
votes
0answers
40 views
Summing with assumptions provides unexpected output
I am computing a closed form of a number of sums having generally the following form: $$ \sum_{i = 0}^{m/2}\sum_{\substack{0\leq k \leq i \\ 2k \equiv i + m \, \text{mod } 3}} k $$
It looks like ...
0
votes
0answers
31 views
Defining a function with certain regularity (e.g. smooth)
My goal is to understand how Mathematica computes limits that would require differentiability assumptions on functions (for, for instance, L'Hopital or Taylor Series).
Consider, for instance, the ...
2
votes
1answer
58 views
Expanding Determinant as Multilinear Alternating Function
I am working with the expression
$$\det\big{|}f(-kx), f(-(k-1)x),\cdots,f(0),\cdots, f((k-1)x), f(kx), g(x)\big{|},$$
where $f,g\colon\mathbb{R}\mapsto \mathbb{R}^{2k+2}$, and want to use the Taylor ...
1
vote
1answer
24 views
2
votes
1answer
31 views
How to state nontrivial tensor symmetry assumptions?
For example dddg, the third derivative of the metric tensor, in dimension $4$.
I need to state that it is symmetric in the first two indices and symmetric in the ...
0
votes
0answers
37 views
Assumptions behavior in Refine[Sin[n Pi/2]] [duplicate]
I don't understand why this first expression returns a correct result:
In> Refine[Sin[n Pi/2], Element[n, Integers] && Mod[n, 2] == 1]
...
0
votes
1answer
40 views
Why does restricting the domain not eliminate this solution?
Beside this specific problem I'm wondering if there's a more explicit way that I can understand when Solve and Reduce will find solutions. I find myself repeatedly getting stuck where I'll get ...
7
votes
1answer
176 views
How to best add assumption that many variables are positive?
I often need to check whether integrals are solvable in closed form and use a notebook with 5ā10 variables that need to be assumed positive. Is there a better way of doing this than adding the clunky ...
0
votes
0answers
41 views
Simplification of symbolic vector and matrices representation
I'm new to the Wolfram Language programming and I cannot manage to do the following.
I wish to use Wolfram Cloud to simpilfy a heavy vector and matrix expression using symbolic complex vectors (...
2
votes
1answer
47 views
Count based hypothesis test for inhomogeneous Poisson process
I am intended to fit the following data using InhomogeneousPoissonProcess[] in v12.0.
The original form of data tabulated given as below
Such a table contains ...
0
votes
1answer
65 views
Mathematica assumptions [closed]
Mathematica produces the answer to integral((x + 5)/(x^2 + x ā 2) dx). Find what is missing and explain
what assumptions it seems that Mathematica is making.
2
votes
1answer
88 views
Why does this boolean computation get stuck?
I want to build a boolean function which takes three one-parametric functions. I really don't know how to write a function for this, but this seems to be working for me as long as the parameter is <...
2
votes
0answers
84 views
Does Assumptions not work on Root objects?
Typically, one can restrict symbolic quantities using Assumptions.
Suppose, for instance, that I want to solve $a=x^2$ for $x$, with $a>0$, restricting my answer to the positive root.
...
1
vote
1answer
57 views
I need to create abstract vectors
$Assumptions = {q \[Element] Vectors[{15}, Reals]};
$Assumptions = {p1[q] \[Element] Vectors[{3}, Reals]};
So I have been using this code in order to define an ...
0
votes
0answers
51 views
How do I apply assumptions to a table of functions
I have a table, really its a tensor but anyways I would like to apply an assumption to it, i.e. 1 - 2 phi[t,x,y,z] == 1 and have it print the tensor after it has ...
3
votes
3answers
124 views
Simplifying square roots of squared reals
I am using Mathematica to check some long, tedious calculations and I am stumped by some mysterious behavior. If I simplify a long expression that clearly has square real factors under a radical, for ...
4
votes
1answer
42 views
Is it better to use a single binary operator in each Assumption entry?
I am trying to understand why
FullSimplify[x^a < 1, {0 < x^a < 1}]
does not simplify but
...
3
votes
1answer
91 views
Display returned integral containing assumptions with integral sign
From solving the PDE example of the general 1 dim heat equation in Nasser Abbasi's site https://www.12000.org/my_notes/pde_in_CAS/maple_2019_and_mma_12/insu157.htm#x182-1810003.1.1 (his problem No 151)...
1
vote
1answer
177 views
Is it possible to use an assumption that a parameter is an odd or even number?
I am trying to integrate:
Integrate[(Exp[x]*(x^m)/((Exp[x] + 1)^2)), {x, -Infinity, Infinity}]
I know that for odd m the result is zero. How can I tell ...
6
votes
1answer
109 views
How to apply assumptions to pattern matching?
I'm trying to remove terms whose exponents are positive in a polynomial.
I tried this one;
Assuming[t > 0, x^t /. {x^a_ /; Positive@a -> 0}]
but the result ...
3
votes
1answer
50 views
Assuming a variable is imaginary
I am confused how to assume a variable is pure imaginary. As a test example, I used the code
Assuming[{ x \[Element] I Reals}, Simplify[x + Conjugate[x]]]
In ...
1
vote
1answer
47 views
Using assumptions, weird output [closed]
I have a Piecewise function, of the type:
$Assumptions = b > a > 0
fun[k_] := Piecewise[{{3k, 0<=k<a}, {k^2, a<=k<=b}}]
fun[a]
When evaluating ...
3
votes
1answer
53 views
Is there a global parameter that limits the number of variables handled by Simplify?
It seems that Simplify is unable to handle (at least some) expressions involving 22 or more variables. Consider the code snippet below:
...
5
votes
1answer
143 views
Simplify is not simplifying a compound inequality as expected
The Simplify command is having trouble verifying a compound inequality, even while it correctly handles the two corresponding single inequalities.
I'm starting ...
1
vote
2answers
61 views
how to get rid of the denominator in the squareroot, that appears in the denominator?
Here is an example: $\frac{\nu y_0}{\left(x_0+\frac{1}{2}\right) \sqrt{\nu ^2+\frac{\left(4 x_0^2+4 y_0^2-1\right){}^2}{16 y_0^2}}}$
...
0
votes
1answer
44 views
1
vote
0answers
42 views
Why does Mathematica miss some solutions for my integral?
When computing the integral of two orthogonal sine functions
$\qquad \sin(n\,\pi\,x)\,\sin(m\,\pi\,x)$, where $n,\,m$ are integers > 0
Mathematica seems to miss the solution where $n=m$. I don't ...
0
votes
0answers
35 views
Using assumptions in DSolve
I want to solve the following differential equation
DSolve[u'[\[Xi]] == a u[\[Xi]]^(2 - m) + b u[\[Xi]] + c u[\[Xi]]^m,
u[\[Xi]], \[Xi]]
with the assumpetion
...
8
votes
4answers
333 views
Simplify makes Mathematica forget that a matrix is Hermitian
Using Simplify with certain trivial assumptions makes Mathematica forget that a given matrix is Hermitian. See the minimal example below:
...
0
votes
0answers
53 views
Dealing with positive power variables in Taylor expansion and assumptions
I would like to compute the Taylor expansion of monomials whose powers are nonnegative rational variables.
First, here is a function which encodes the multivariate Taylor expansion at the points <...
0
votes
1answer
62 views
Using Assumptions [closed]
Iām trying to use Assumptions for the set of variables in a form:
$Assumptions = {(k, z) ā Reals, (k, z) > 0};
But as a result a receive an errors. What is ...
2
votes
2answers
86 views
Definite Integration with Exponental Heaviside Step Funtions
As part of an equation of state calculator that I am working on, I have to handle a virial expansion for the equation of state. As such I have to solve for the virial coefficent, $B(T)$, which is ...
0
votes
1answer
48 views
How to use assumptions without Simplify[]?
According to this simple example program, the assumptions evaluated only with the Simplify[] function call. However, I wouldn't like to use Simplify[] because it can be very slow with longer ...
0
votes
0answers
38 views
Solving an integral using assumptions
I am trying to solve the integral
Integrate[(Sin(theta))/sqrt((r^2) + (s^2) - 2 rs(cos(theta))), {theta, 0, pi}]
with assumptions that ...
0
votes
1answer
84 views
Domain specifications for InverseFunction
I have difficulty implementing on how to specify the domain that I want for ry which is the inverse function of rho. The necessary condition is that, $\textbf{ry}$ must remain $\textbf{positive}$ for ...
