Questions tagged [assumptions]

Questions about the function Assuming[], the $Assumptions system variable, and the Assumptions option of functions such as Simplify[] and Integrate[].

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3
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1answer
62 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, ...
10
votes
2answers
498 views

Assumptions allowing to calculate an elliptic integral

When I feed Mathematica the following integral: Integrate[Sqrt[(A - x) (B - x)/x], {x, 0, B}] it spits it back out without evaluating it. However, it can ...
0
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1answer
50 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: ...
12
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5answers
518 views

Limit of sequence of functions behaving strange

I'm trying to determine the limit of the sequence of functions $$f_n(x)=\left(\frac{1}{\pi}\arctan(n x) + 1/2\right)^n. $$ I define ...
0
votes
1answer
49 views

Handling Errors in Slowly Converging Dirichlet Beta Infinite Sum

I have tried to calculate the following slowly converging double sum in Mathematica 11.3 $$\sum _{k=1}^{\infty } \left(\frac{ 1}{(2 k-1) (2 k+1)} \left(\sum _{n=1}^{\infty } \frac{(-1)^{n-1}}{(2 n-1)...
0
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1answer
43 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
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0answers
90 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
68 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
62 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
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0answers
37 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
57 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 ...
2
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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 ...
14
votes
3answers
3k views

Logarithm of exponential [closed]

Ok, this is awkward. E^Log[a] gives a, which is what I expected, BUT, Log[E^a] is not ...
2
votes
0answers
150 views

Getting long complex-valued integrals when simpler real-valued expressions exist

I have a long list of real-valued functions I'd like to integrate symbolically. For many of them, Mathematica gives me results with long complex-valued expressions involving weird functions such as <...
1
vote
1answer
24 views

Assumptions in Integrate not working properly

I have the following code: ...
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
39 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
174 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 5–10 variables that need to be assumed positive. Is there a better way of doing this than adding the clunky ...
0
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0answers
39 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 (...
1
vote
1answer
54 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 ...
1
vote
1answer
44 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
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1answer
65 views

Mathematica assumptions [closed]

Mathematica produces the answer to integral((x + 5)/(x^2 + x − 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. ...
10
votes
1answer
1k views

Is my expression too complicated for FullSimplify or am I doing something wrong?

I have a messily defined function $v(h, w)$ with $h, w \in \mathbb{R}$ and with a removable singularity at $h=1/2$, and I am trying to prove some of its properties using Mathematica. In particular I ...
4
votes
2answers
87 views

Getting around symbol favoritism of Simplify and FullSimplify [duplicate]

Simplify may or may not simplify depending on the symbols you use for its assumptions are good. For example, here is a case where ...
0
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0answers
49 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 ...
5
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)...
2
votes
1answer
1k views

How Simplify and Assume can be combined on matrix products?

What I am trying to do is to simplify some expressions involving matrices! The problem is that Simplify[] considers the simplifications based on alphabetical order and everything is Commutative. For ...
1
vote
1answer
161 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
49 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
60 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
2answers
91 views

Result with assumptions contradicts previous result

Without assuming anything on the argument of the complex number inside the Gamma function ...
0
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1answer
44 views

Exits and beeps on Integration

Evaluating ...
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 ...
7
votes
0answers
254 views

What is a “generic case”?

Introduction With this question I am coming back to a long-standing issue I have with Mma's concept of a "generically correct" result. The basic idea seems to be, vaguely, that if a result is true in ...
0
votes
0answers
31 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 ...
0
votes
1answer
83 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 ...
8
votes
4answers
325 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
60 views

Using Assumptions [closed]

I’m trying to use Assumptions for the set of variables in a form: $Assumptions = {(k, z) ∈ Reals, (k, z) > 0}; But as a result a receive an errors. What is ...
2
votes
2answers
85 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 ...

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