# Questions tagged [assumptions]

Questions about the function Assuming[], the $Assumptions system variable, and the Assumptions option of functions such as Simplify[] and Integrate[]. 494 questions Filter by Sorted by Tagged with 0 votes 1 answer 40 views ### Need help with Assumptions for an integral I want to solve this Log, Integrate[2a Log[-a+((A0 + (y-y1)²)^½, {y1, 0,b}] But Mathematica only gives me long conditional expressions or imaginary numbers. I (my thinking which can be wrong) assume I ... • 1 5 votes 3 answers 133 views ###$Assumptions = _ ∈ Reals results in incorrect simplification of ConjugateTranspose[..]

The linear combination $Q$ of two Hermitian matrices $A^\dagger = A, B^\dagger = B$ with real coefficients $m,n \in \mathbb{R}$, i.e. $Q = m A + n B$ is itself a Hermitian matrix $Q^\dagger = Q$. ...
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### Struggling to get Solve to accept assumptions

I can't get Solve to solve the following two equations under the appropriate assumptions. When I enter ...
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### Assuming one variable is greater than another variable

I want to add the assumption that M>m, but I am not sure how to do that. I tried Assuming[M > m, M > m] But this ...
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This question derives directly from this one, but concerns instead a different matter... one related to display format. This integral $$I = \int\limits_2^4 \frac{\sqrt{\log (9-x)}}{\sqrt{\log (9-x)}+\... • 36.7k 8 votes 1 answer 219 views ### Why Mathematica is treating the product of (specified) real variable as complex? For the given matrix ... • 539 4 votes 1 answer 48 views ### Proper usage of Assuming statement I want to evaluate a command under an assumption, and thought Assuming was the right way to go. Suppose we want to calculate a Matrix rank. Following the second ... • 251 0 votes 0 answers 27 views ### Put an initial condition on some parameter Good morning, I'm new in the world of Mathematica, so I'm sorry if my question isn't very relevant. I'm trying to solve a system of 5 equations withs many parameters. To be clear, I will hit the core ... • 101 5 votes 2 answers 101 views ### Simplifying expressions with nested square roots When I run FullSimplify[Sqrt[(1 - Sqrt[1 - 2 x^2 y^2])^2], {1 > 2 x^2 y^2 > 0}] I obtain 1 - Sqrt[1 - 2 x^2 y^2]. However,... • 385 2 votes 2 answers 110 views ### Why is my integral with the error function not being evaluated? I'm new to Wolfram Mathematica and I was trying to evaluate this integral in particular:$$\int_{0}^{x}\frac{e^t \operatorname{erf}(\sqrt{t})\sqrt{\pi t}+1}{\sqrt{\pi t x -\pi t^2}}\mathrm dt$$The ... 2 votes 1 answer 95 views ### Integrate ignoring assumptions I want to evaluate an integral with all variables real and positive. Specifically, ... • 127 1 vote 2 answers 103 views ### Argument of a complex number with assumptions I am trying to calculate the argument of a complex number: Arg[Cos[y]*Exp[I x]] where both x and y are real. The solution is clearly x, but I can't get it with ... • 51 4 votes 2 answers 103 views ### Simplify with False assumptions gives wrong answers Simplify is very gullible: if it gets a False assumption, it'll believe anything is True: <... • 18.3k 6 votes 3 answers 127 views ### Extracting a logarithmic divergence of an expression using Series Consider the following expression: ... • 1,249 1 vote 1 answer 33 views ### Getting the same result from Integrate as Probability I'm trying to solve a Baysian inference problem (although the details are not all that important for this question) I define two probability distributions P and <... • 819 0 votes 2 answers 45 views ### Assuming combined with mathematical notation of Integrate I am trying to write down the following expression Integrate[Exp[-a/2/x]/x/(x + 1), {x, 0, b}, Assumptions -> a > 0 && b > 0] using mathematical ... 0 votes 0 answers 38 views ### Integer parameter assumption gives incorrect result when integrating There are some dangerous pitfalls that can happen when evaluating some integrals, assuming that some parameters are integers. For example, consider the following: ... • 1,249 0 votes 2 answers 87 views ### Assumptions in Integration for positive real values [closed] I want to evaluate the following integral in Mathematica.$$ \int_0^\infty \frac{a^{-t}-b^{-t}}{t} dt = \ln \left(\frac{\ln b}{\ln a} \right)$$I try to enter this, but Mathematica can't figure it out.... 1 vote 0 answers 39 views ### How to declare at the beginning of the notebook that a variable belongs to a set? In the notebook I am working on I have certain symbolic variables (e.g., c and r) which I would like to declare since the very first few lines to be non negative real numbers. Correct me if I am wrong ... • 53 2 votes 1 answer 47 views ### How to use SystemPrivateAssumptionAccess and Assumptions*? I see this function is used by some symbols in Assumptions*, and it HasDownCode and does not ... • 2,168 3 votes 1 answer 272 views ### Mathematica tries to differentiate Abs[x] and this causes a problem? [duplicate] I am trying to run the following code: ... • 4,911 0 votes 0 answers 40 views ### Global assumption non zero I would like to define globally an assumption stating that I have a nonzero real vector v. For now, I put : Assumptions = Element[v,Vectors[{100},Reals]] but v ... • 442 2 votes 1 answer 78 views ### Simplifying an expression with complex conjugates I have been unable to do the following. First I make an assumption Assumptions = x \[Element] Reals; and define ... • 79 1 vote 1 answer 56 views ### Why does not ContourPlot consider the condition given in RegionFunction in the given code? I have two functions f(x,y) and g(x,y). I am using RegionFunction in ContourPlot to see those values of (x,y) for which ... • 463 2 votes 2 answers 96 views ### Is it possible to exclude a condition, say, f(x,y)=const., from a ContourPlot code? ... • 463 4 votes 2 answers 374 views ### How to get a manipulated plot of the intersection points of two curves without finding them numerically? I have four 2-variables functions for 0<x<3 and 1<y<3 ... • 463 2 votes 1 answer 65 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. ... 0 votes 1 answer 61 views ### Adding Assumptions in double integral written in "math input" mode I've the following double integral and I'd like to write Assumptions->Re[c]>0, but if I try to do it, I get a syntax error. How can I add the above condition but without changing the ... 0 votes 0 answers 39 views ### How to make assertions for subscripted variables? I'm trying to write a formula using subscripted variables like x₁, x₂, x₃, ..., so that I can later retrieve their values programmatically. However, I'm struggling ... • 101 0 votes 1 answer 211 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 ... • 663 0 votes 0 answers 66 views ### Can I use assumptions to declare a variable's type? I'm trying to declare P as a vector. I searched for a while, the closest way seems to be Assumptions: ... • 174 1 vote 2 answers 49 views ### How to assume some variables to "not" be a function of other variables at the time of defining a function [closed] I have a function with the following definition: F[x]=Exp[q*w*x]; I want to take total derivatives of F. How can I define that q and w are not dependent on x at the ... • 350 0 votes 0 answers 68 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 ... • 127 2 votes 0 answers 104 views ### Why does this ConditionalExpression appear? [closed] I am new to Mathematica. Could anyone help explain why ws > 0 appears in the solution? How to define symbolic variables' range? Thanks! EDIT to include code <... • 43 0 votes 2 answers 100 views ### How to solve system of equations with complex variables I'm trying to obtain the solution to the following system of 3 equations and 4 variables: ... 1 vote 1 answer 78 views ### How to 'define' value in Assumptions but not let Simplify replace it? [closed] I want to let Simplify know the exact value of a symbol, to resolve logical statements, but don't want it to actually replace it. For instance, I would like ... • 353 0 votes 1 answer 55 views ### Get Real Solutions works in Solve but PositiveReals don't (Quantities) I'm trying to get the R+ Solutions to a school problem with solve. Everything works fine with Dom -> Reals but when I try ... 2 votes 0 answers 67 views ### Defining new Domain for variables I am trying to define a new Domain for variables to use with functions like FindInstance or Solve. For example, If I wanted to solve x+y+z=1 over the Reals, I'd get a large solution space. But If I ... 1 vote 0 answers 50 views ### TensorExpand ignores assumptions? Here's a minimal example to demonstrate my problem: ... • 215 1 vote 1 answer 82 views ### Simplify an expression with assumptions connected with OR Mathematica doesn't seem to have any problem with these commands: ... 4 votes 1 answer 250 views ### Why isn't this expression returning true to being positive when it is clearly positive? Consider: ... • 487 0 votes 0 answers 44 views ### Test domain assumption of a variable Using Assumptions to define the domain of variable is straightforward, i.e. Assumptions = Element[x, Reals]. Nevertheless, it'... • 304 4 votes 1 answer 150 views ### Representing number domain by a symbol [closed] I'd like to represent the number domain by a symbol rather than text word. While Solve[n^2 - 19 n + 99 == k^2 \[And] {k, n} > 0, {k, n}, Integers] works fine, I'... • 36.7k 4 votes 3 answers 1k views ### How can I specify the assumption 'a' is much greater than 'b' (a>>b) in Mathematica? I want to evaluate an expression of type 1/(r-2 m), assuming r >> 2 m. This is regarding black hole physics and r = 2 m is the Schwarzschild radius. But I am working on something where I need to ... • 247 1 vote 0 answers 55 views ### Piecewise and Assumptions [closed] Assumptions sometimes work as expected with Piecewise, for example Simplify[Piecewise[{{A, a + b >= c}, {B, True}}], Assumptions -> a + b > c] correctly ... • 501 1 vote 1 answer 76 views ### Solving generating conditional expression despite assumptions ... 0 votes 2 answers 76 views ### Triple integral: How do I include assumptions and conditions? I would like to solve the following integral:$$I=\int_{0}^{a} \int_{0}^{y} \int_{0}^{z} e^{(a-x)^{3}} d x d z d y$$with the condition that:$$a>0 So I tried to input the equation like below ... 208 views

### Why Mathematica is not assuming real variable as real?

I am dealing with the situation where despite of specifying my variables b1 and c to be greater than zero, Mathematica still ...
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### how can I modify this function to convert to polar form for any complex expression?

The function from another post is to convert a complex number to polar form. polarForm = Expand[# /. z_?NumericQ :> Abs[z] Exp[I Arg[z]]] & Now if I apply ...
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