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You also have pieces of Maple online here: http://www.maplesoft.com/products/StudentApps/index.aspx


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Use wolframalpha for that. The following input gives eigenvalues depending on parameters $a,b$: eigenvalues {{4,a},{b,-1}} Here a link.


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You can try Magma, which has special code for dense systems: http://magma.maths.usyd.edu.au/users/allan/densef4/


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The command "pdsolve([pde]);" can solve this system of partial differential equations.


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This is an atempt to solve the PDE system, leading to : $$y(a,b,c)=F\left(a\,c\,b^{\frac{1}{2}}+\frac{3}{5}b^{\frac{5}{2}} \right)$$ with $F$ arbitrary derivable function until no bounding condition is specified.


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This approach is heuristic, but it gets you a solution. The first and third equations, derivatives with respect to $a$ and $c$ integrate out the same, so it makes sense to let $u(a,b,c)=u(b)$. You can get a solution by assuming that $u(b)=b^n$. Then you have to solve for the right value of $n$ to make the derivatives match an exact differential.


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The solve command can handle multiple inequalities and equations. Write your range as inequality restrictions on your variable. Input either a set {} or a list []. Example: ineq := cos(x)>1/2; myrange := x > 2*Pi, x<4*Pi; solve({ineq,myrange},x); Output: $$\left\{ x<\frac73\,\pi ,2\,\pi <x \right\}, \left\{ x<4\,\pi ,\frac{11}3\,\pi ...


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I use: http://www.nu-math.com/omega It is free. There is a quick reference to get you started: http://www.nu-math.com/nhome/qr.jsp Here is an example: m:matrix([2,-1], [3,4]); charpoly(m, x); solve(%, x);


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We may use the Chinese remainder theorem and compute $F_{2^{100}}\pmod{5^{30}}$ and $F_{2^{100}}\pmod{2^{30}}$ by exploiting the properties of the associated Pisano periods (for instance, the period of the Fibonacci sequence $\pmod{5^n}$ is just $4\cdot 5^n$) or consider that it is simple to compute $(F_{2k},L_{2k})$ from $(F_k,L_k)$, since: $$ F_{2k} = F_k ...


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The function ${\rm abs}$ is continuous on all of ${\mathbb R}$, hence should have primitives $F$ defined on all of ${\mathbb R}$. Given that ${\rm abs}$ is "special" at $x=0$ we should look for the primitive obtained by integrating from $0$ to $x$. In this way we obtain $$F(x)=\int_0^x |t|\>dt=\int_0^x t\>dt={x^2\over2}\qquad(x\geq0)$$ and ...


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Recommendations for Commutative Algebra Software? CoCoa Singular Macaulay2 where the example usage about CoCoa is GR basis like How to analyse a sparse adjacency matrix. Graphs visualised with examples Atlas visualisation like here with NetworkX for different polynomials Random geometric graph with NetworkX giant component here ego graph ...


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A great site is GeoGebra. It starts in 2D by default, but you can click on a settings button on the right to open a 3D viewer. You can add a point anywhere on the page then double-click it to set its coördinates. There are many tools, including drawing the plane determined by three given points. One of the pleasures of this site is that you can drag any of ...


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It is unclear if your question is about arbitrary curves or arbitrary functions. A curve can be intersected by horizontals/verticals as many times as you want, and can be freely rotated. It can be described by parametric equations $$x=f(t),y=g(t).$$ A function needs to be univocal, i.e. at most one $y$ per $x$; rotating a function doesn't make sense. It ...


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Pretty much any drawing or CAD program can do the curve manipulation you described. This includes Inkscape, Adobe Illustrator, AutoCAD, CorelDraw, or even Powerpoint. In most cases, these programs create cubic Bézier curves. If you want to get the equation of the curve, the first step is to get the "control points". There are four of these for each ...


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It sounds like you're talking about drawing Bézier patches. Lots of programs let you draw these (e.g. essentially every graphic design program) and all of them would have an internal representation of the equation, although I'm not sure how to get most of them to tell it to you. But that should tell you what to Google. I found this thing online: ...



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