algebra

What is a formula to get a three dimensional vector B lying on the plane perpendicular to a vector A? That is, given a vector A, what is a formula f(angle,modulus) which gives a vector that is perpendicular to A, with said modulus and rotated through an angle? If the two vectors are perpendicular then their dot product is zero. So: v1(x1, y1, z1), v2(x2, y2, z2) . => x1 * x2 + y1 * y2 + z1 * z2 = 0 You know (x1, y1, z1) . Put arbitrary x2 and y2 and you will receive the corresponding z2 : z1 * z2 = -x1 * x2 - y1 * y2 => z2 = (-x1 * x2 - y1 * y2) / z1 Be aware if z1 is 0 . Then you are in the

I was doing the mathematical calculations with python or octave because of availability of really nice functions and libraries at hand. But recently I gained interest in ruby and I wonder if there is an equivalent in Ruby to the numpy, scipy in Python for scientific programming. Specifically, I'm looking something that I can draw plots as in matplotlib and do mathematical, algebraic calculations quickly as in numpy and scipy. Linear algebra is at the heart of most large-scale scientific computing. LAPACK is the gold standard for linear algebra libraries, first written in FORTRAN. There's a

Can you advise me some flexible and powerful, yet fast library which could cover SciPy (both in performance and functionality). I found SciPy very expressive - but I want to try something in Scala. I read a little about Scala - but is not as featured as SciPy. Any alternatives? Maybe Java library? The functionality in Scipy is rather Matlab-like. So the question is whether you just want the core linear algebra / vector-matrix mathematics operations, or all sorts of things like clustering. If you are not aware of both Scalala (now called Breeze ) and ScalaLab , you should check them out--maybe

For any whole number input W restricted by the range R = [ x , y ], the "overflow," for lack of a better term, of W over R is W % (y-x+1) + x . This causes it wrap back around if W exceeds y . As an example of this principle, suppose we iterate over a calendar's months: int this_month = 5; int next_month = (this_month + 1) % 12; where both integers will be between 0 and 11, inclusive. Thus, the expression above "clamps" the integer to the range R = [0,11]. This approach of using an expression is simple, elegant, and advantageous as it omits branching . Now, what if we want to do the same thing

Is there any algorithm that can find the sign of an arbitrary symbolic algebraic expression given in a "Tree - Form"? I know that a general algorithm doesn't exist because the zero recognizion problem is undecidable for an arbitrary expression, but how should I approach the problem of finding the sign of an expression? (how is this done in computer algebra?) For example: sign(sqrt(2)-1) = ? Evaluate the function value You need function evaluator engine for that (it is not that hard to code) there is no way to evaluate sign only if you want to support +,- operations !!! All my function

I'm having a mental block here, and algebra not really being my thing, can you tell me how to re-write the JavaScript code below to derive the variable, c , in terms of a and b ?: a = Math.pow(b, c); c = ? Thanks! c = Math.log(a)/Math.log(b) Logarithms. You want the logarithm of a. B is the base, c is the exponent, so log b a = c 来源： https://stackoverflow.com/questions/4016213/whats-the-opposite-of-javascripts-math-pow