Questions tagged [assumptions]
Questions about the function Assuming[], the $Assumptions system variable, and the Assumptions option of functions such as Simplify[] and Integrate[].
428
questions
2
votes
0answers
54 views
Unexpected results with Integrate/AsymptoticIntegrate with assumptions
I am quite disturbed by the result provided by Mathematica, and I am not sure if I understand perfectly its behavior.
What I want to do is to check the asymptotic form of the function $I(\tau)$ with $\...
0
votes
0answers
42 views
How to assume a number to be a half integer?
For integer x $\left(\cos 2\pi x\right) ^2=1$ and I can check this as follows
...
0
votes
2answers
71 views
1
vote
0answers
78 views
How reliable is AsymptoticIntegrate?
In new mathematica 12 there is a new function AsymptoticIntegrate. However, it seems that it gives me incorrect results in some cases. To be completely honest, it ...
11
votes
2answers
275 views
Behavior of Solve with $Assumptions changed in 12.2
Something changed with Solve between versions 12.1 and 12.2.
12.1:
...
2
votes
3answers
336 views
How can I write in Mathematica that 2*x is an integer? [closed]
I have to maximize $h/k^2$, where $h/k^2 < 0.1974$ and $k$ is an integer, and $2\cdot h$ is an integer, $h>0$, $k>0$.
How can I write this problem in Mathematica?
0
votes
0answers
76 views
Issue with several replacements in a function under certain conditions
I am trying to define a function (reduce[x]) which does several substitutions, depending on the values of certain parameters. Concretely, consider an expression x, which contains an arbitrary number ...
0
votes
1answer
45 views
How do I give assumptions to Simplify or Solve? [closed]
I've have the expression:
q2sol =
(Sec[2*a1]*Tan[a1]^3*(-7 + 6*Cot[a1]^3*Sqrt[Tan[a1]^2]))/(6*Sqrt[Tan[a1]^2])
I know that a1...
0
votes
0answers
17 views
Assumptions with piecewise problem?
I am trying to apply the assumpion of 0<s<1 throughout the calculation however the piecewise condition does not accept it automatically. Is there any way to avoid the manual choice of x>0.
...
1
vote
0answers
62 views
Assuming a monotonic function
I'm trying to tell Mathematica that a function is increasing. More specifically, I would like at least one of the following statements to report 'true'.
...
0
votes
2answers
47 views
Expression simplification
I have this term
Sqrt[(B Bc)/(A^2-B Bc)]Sqrt[B Bc+A(-A+Sqrt[A^2-B Bc])]Sqrt[-B Bc+A(A + Sqrt[A^2-B Bc])],
which actually can be simplified to B*Bc. However, it ...
2
votes
1answer
63 views
Trouble evaluating this definite integral, either directly or with indefinite + limits
I have the function
$$
\Sigma(x) = \frac{\sqrt{R^2-x^2}(\left| R\right| -1)}{\left(R^2-1\right) \left(x^2-1\right)}+\frac{\tan ^{-1}\left(\frac{\sqrt{R^2-x^2}}{\sqrt{R^2 \left(1-x^2\right)}}\right)-\...
0
votes
0answers
31 views
Simplify with Assumptions: Puzzle for 4 variables [duplicate]
I have a rather specific question about Simplify[] (hope this is not off-topic).
The puzzle I have is that Simplify[] with ...
2
votes
2answers
57 views
Solving an Algebraic Equation with Constraints on Multiple Parameters
Suppose we have the following equation to solve (with respect to $x$):
$$
\frac{m\omega^2x^2}{2} + \frac{m\alpha x^3}{3} = E,\quad\text{where }m,\omega,\alpha,E>0\text{ and } E < \frac{m\omega^6}...
0
votes
0answers
27 views
Why a complementary inequality for function values does not simplify to False?
I have a general assumption of a function to be positive. The direct inequality (f[x]>0) does simplify to True, but a complementary one (f[x] < 0) does not simplify at all despite the fact that ...
0
votes
1answer
60 views
How can I get rid of Abs?
In the following code, the functions WP[t] and WS[t] are real. Time also is a positive parameter. As you can see, MATHEMATICA enters Abs in the calculations. Including Abs only complicates the next ...
2
votes
1answer
90 views
Mathematica and its default assumptions
I am a bit surprised that evsluating
Integrate[Exp[I n x],{x, 0, Pi}]
gives
$\qquad \frac{-i(e^{in\pi}-1)}{n}$.
What if $n = 0$? I didn't assume anything about $n$ ...
1
vote
1answer
51 views
Use the fact that $u(t)\cdot u'(t)=0$ for $u\in\mathcal{S}^2$
If for all $t$, $u(t)$ is a point on the unit sphere $\mathcal{S}^2 \subset\mathbb{R}^3$, $u'(t)$ is orthogonal to $u(t)$, because $u'(t)$ is in the tangent plane of the sphere.
I have large ...
1
vote
3answers
277 views
Problems with solutions involving Lambert W function of transcendental equation
Solve and Reduce fail here with rational parameter l, but succeed when I plug in a value
<...
8
votes
1answer
109 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
56 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
75 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
51 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
65 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
40 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
72 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
62 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
47 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
36 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
100 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
76 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
66 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
49 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
32 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
61 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
27 views
2
votes
1answer
33 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
44 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
185 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
votes
0answers
45 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
56 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
87 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 <...
3
votes
1answer
122 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.
...
0
votes
2answers
101 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
58 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
130 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 ...
