# Tagged Questions

Questions about the function Assuming[], the $Assumptions system variable, and the Assumptions option of functions such as Simplify[] and Integrate[]. 1answer 557 views ### Prove (or check) an expression is positive given constraints on variables? I'm trying to figure out whether an expression is always positive given positive parameters. When the expression is complicated, I can't do this by eye. Is there any way to make Mathematica prove (... 1answer 250 views ### How to study the sign of an expression including a function, with conditions on the function? I'm trying to study the sign of an expression, having information on some of my parameters. I don't know how to code these conditions. For example, I want to know when this expression: ... 3answers 806 views ### DSolve will not apply assumption m ∈ Integers I am trying to solve a linear second order ODE using DSolve which involves an arbitrary integer m. ... 3answers 150 views ### Evaluating an expression assuming a value for a variable only in the local context Imagine we wish to evaluate some expression like NIntegrate[x^2*q,{x,0,100}] assuming some value for q like ... 1answer 153 views ### Mathematica does not respect tensor order? I'm trying to verify an identity involving symmetric traceless tensors over the reals. What I tried was: ... 4answers 193 views ### Cancelling units in two-argument ArcTan Consider ArcTan[3, -3] (* out: *) -Pi/4 ArcTan[3 a Sin[t/2], -3 a Sin[t/2]] (* out: *) ArcTan[3 a Sin[t/2], -3 a Sin[t/2]] However, we can fix the ... 1answer 251 views ### Impose an specific Trigonometric expansion with TrigExpand Is there a way to impose in mathematica an specific trigonometric expansion with TrigExpand? I have various double-angle expressions for cosine and sine in my ... 2answers 349 views ### Why doesn't Abs simplify further? Why does this: Simplify[Abs[x + I], Element[x, Reals]] give me Abs[x + i] Is there a way to force Mathematica to give me ... 1answer 227 views ### Simplifying complex expressions I'm trying to work with complexes and I want Mathematica to know that all variables are real unless I explicitly assigned the variable with an I so I wrote: ... 1answer 467 views ### Are greek symbols causing different evaluation? I've updated today to Mathematica 9.0.1.0 from version 8 and found something that absolutely confuses me. Let us define a piecewise function: ... 2answers 130 views ### Inconsistent results for equivalent converging symbolic integrals I have looked at previous questions and I'm aware that this seems to be a known bug: Mathematica giving inconsistent results for symbolic integrals done in different ways. The origins for the bugs ... 0answers 96 views ### When and why are Assuming and Assumptions not equivalent? [duplicate] In this question there's an example of an integral where using Assuming and Assumptions give different results: ... 1answer 420 views ### Problem with limit that requires L'Hôpital's rule to compute Consider the following limit. Limit[(a - Sqrt[a^2 + x])/(a^2 - a*Sqrt[a^2 - x]), x -> 0, Assumptions -> {a > 0}] Mathematica 9.0.1.0 gives ... 1answer 74 views ### One more question about Assumptions and Integrate There are many questions about assumptions here. Many of them are problem specific. That is why I want to ask a question in the most general way. Why does Mathematica solves this ... 1answer 80 views ### How can we tell Series to treat the expansion parameter as an integer? It is simple for Mathematica to find an asymptotic expansion for$\frac{1}{-1+p}$as$p \rightarrow \infty$. However, if we want to restrict$p$to be an integer and also include some terms that ... 1answer 239 views ### Re[x] vs. x ∈ Reals in the context of Assuming Let's say that$x$is some real valued number$>0$. Are the following commands interchangeable in the context of using Assuming? ... 0answers 86 views ### How does TensorReduce use assumptions? I would like to use TensorReduce by assuming that certain patterns of functions are tensors. From documentation of TensorReduce: ... 2answers 146 views ### Simplification with assumptions I'm trying to make Mathematica do some simplifications for me. I have the expression ((1 + s[1]) (-1 + s[2]) )/(-1 + s[1] s[2]) and want to simplify this with ... 1answer 114 views ### Simplifying using assumptions Is there a way to simplify the following equation (-p(a-x)((a-b)P(b-x)+Q(b+x)(a-b+2x))+q(a+x)(-(a-b)Q(b+x)+P(b-x)(-a +b+2x)))/((b-x)(-a + x)(a+x)(b+x)) assuming ... 2answers 283 views ### RSolve with assumptions I want to solve the following non-linear first order difference equation: $$k_{t+1} = (1-a) k_t^{a}$$ with$0 < a < 1$, and$k_0 = \text{const.}$. Of course, the solution is easily found, ... 0answers 303 views ### Simplify and Sqrt, inconsistent behavior? I have encountered some problems when using Simplify with expressions containing a square root and isolated a following test case ... 3answers 463 views ### Reduce can't reduce an equation without appropriate assumptions When there are three unknowns (x, y, z), Mathematica can solve it: ... 2answers 158 views ### FullSimplify used with Assuming giving unexpected results Can someone shed some light on why Assuming[{x ∈ Reals}, x (Sign[x]^2 - 1)] // FullSimplify returns x (-1 + Sign[x]^2) ... 2answers 118 views ### Assumptions within Simplify I am using the ratio between two error probabilities in various functions. I want Mathematica to display this ratio in the most simple manner. How do I let Mathematica know that, in this case, the ... 1answer 144 views ### Assumptions in mathematica when Symplify on Log[Exp[a/b]] In mathematica 9.0: This: Assuming[b > 0 || b < 0, Simplify[Log[Exp[a/b]]]] yields: a/b However, this: ... 1answer 339 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 ... 1answer 393 views ### Use Pattern with Vectors in Assumptions I had a problem using Pattern with Vectors in Assumptions. Here's how I use ... 3answers 247 views ### Assumptions for RotationMatrix I'm making C++ program, and in my program I need a rotation matrix around any vector. I wanted to extract RotationMatrix[fi,{x,y,z}] output and put it in my program.... 1answer 210 views ### Assumptions about list elements I am trying to simplify some expressions using assumptions and got an inconsistent behavior of Mathematica 9 when working with indexed variables. Consider ... 1answer 237 views ### Can't simplify Abs[a*Cos[x]]^2 Why doesn't FullSimplify[ Abs[a*Cos[x]]^2, Assumptions -> {{a, x} ∈ Reals}] simplify to (a*Cos[x])^2 but this query <... 2answers 112 views ### How to add a condition to a formula so that it will not appear at the result? [duplicate] Sometimes I have very long and complicated equations, when I evaulate the equations for example taking derivative or integral there will be several conditions with the answer. My question is that; is ... 1answer 339 views ### How to select TransformationFunctions based on Assumptions made when using Simplify? I am re-writing the question using a very simple example so not to confuse matters with the another question being asked where I used the example from there. In general, how to add logic to switch ... 1answer 2k views ### Use of$Assumptions [duplicate]

I don't really understand the behaviour and the usage of $Assumption. For instance, when I set$Assumptions = λ > 0, I expect ...
2k views

### Simplifying expressions with square roots

I would like Mathematica to simplify this expression: $4 \left(16 \sqrt{\left(-1+2 c^2\right)^2}-32 c^2 \sqrt{\left(-1+2 c^2\right)^2}+\sqrt{\left(1-8 c^2+8 c^4\right)^2}\right)^2$ ...
199 views

### Keeping Integrate from making unnecessary assumptions

I would like to evaluate the integral $\int_{-\infty}^\infty \mathrm{d}x \, \exp\left(- a x^2 - x^4\right)$ for any real value of $a$. Mathematica 8.0.4 gives the following result: ...
172 views

### Double Integral and Assumptions

I'm afraid this is going to be a really stupid question. Evaluating the following definite integral Integrate[Sqrt[1 - (x^2 + y^2)], {x, -1, 1}, {y, -1, 1}] ...
142 views

### How to tell Mathematica to make assumptions? [duplicate]

Say I want to integrate 1/(x^2+a^2) and I want Mathematica to know that $a>0$. What would be the command? Something like: ...
711 views

### I can't solve this set of equations

I am having trouble solving a set of equations using Mathematica 8. I do not get any errors, but I don't get any solutions either. My parameters and variables are real and non-negative. ...
151 views

### Strange behavior of Integrate

I'm trying to calculate the following integral using Mathematica 9.0.1.0 a11=Integrate[Abs[Sin[b+x]],{x,0,2*\[Pi]}] This should be a simple problem; however, it ...
147 views

### Assuming monotonicity and concavity

I have an expression that I would like to evaluate: 2 phi''[1 + a (-1 + u[10])] phi'[q]^3 > phi''[q] phi'[q] phi'[1 + a (-1 + u[10])]^2 Is there any way of ...
3k views

### How to take conjugate of a function?

Naïvely this is what happens and it obviously is not helpful! ...
671 views

### Assume function is real valued

I want to create a function returning subscripted symbols and I want these symbols to be assumed real. How do I do that? ...
895 views

### Why does Integrate declare a convergent integral divergent?

When I try this command Integrate[1/Sqrt[(s^2 - u)^2 - 1], {s, m, Infinity}, Assumptions -> u > 2 && m > 10] Mathematica declares that the ...
77 views

### Restricting a plotted expression to reals in a Manipuate

I have an expression from which I'm trying to create a plot that I can manipulate. The expression contains Abs, and I only want to have it evaluated for reals. What ...
2k views

### Is it possible to impose “Assumptions” in DSolve or equivalent? (differential equation solving)

When DSolve tries to solve differential equations, it is sometimes not smart enough to generate conditions according to different possible value of parameters. ...
170 views

### Simplifying Complex Numbers that contain physical units

I am trying to evaluate the following: Simplify[Meter Nano Re[(a + I b)/(Meter Nano)], Assumptions -> Element[{a, b}, Reals]] However, Mathematica returns: <...
5k views

### How can I use assumptions with FindRoot?

I have something like FindRoot[f[x], {x, a}] Now I want FindRoot to constrain the solutions to 0 < x < 1. How can I ...
3k views

### Usage of Assuming for Integration

For some reason, when I enter the following integration in Mathematica Assuming[{k ∈ Integers}, Integrate[ Exp[ I k t], {t, -π, π}]] the result turns out to be 0....