rws's profile - activity

It sometimes helps to expand and factor:

sage: s
1/4*(2*D*Nb*Pmean - (D*H*alpha + D*H)*c)/((alpha + 1)*c)
sage: s.expand()
-1/4*D*H*alpha/(alpha + 1) - 1/4*D*H/(alpha + 1) + 1/2*D*Nb*Pmean/((alpha + 1)*c)
sage: _.factor()
-1/4*(H*alpha*c - 2*Nb*Pmean + H*c)*D/((alpha + 1)*c)
sage: _.partial_fraction()
1/4*(2*Nb*Pmean - (H*alpha + H)*c)*D/((alpha + 1)*c)

sage: print([SQ[i*2][0].minpoly().degree() for i in range(16)]) [32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32]

Simplification: sin(atan(y)) = y/sqrt(1+y^2) could be applied.

Using the actual function I get a fine plot via:

sage: CDFlogn(x,nu,sigma) = 1/2*(1+erf((log(x)-nu)/(sigma*sqrt(2))))
sage: plot(CDFlogn(x,1.5,.6),0,10)
Launched png viewer for Graphics object consisting of 1 graphics primitive

sage: CDFlogn(x,1.5,.6)
1/2*erf(-0.833333333333333*sqrt(2)*(-log(x) + 1.50000000000000)) + 1/2
sage: CDFlogn(4,1.5,.6)
1/2*erf(-0.833333333333333*sqrt(2)*(-log(4) + 1.50000000000000)) + 1/2
sage: CDFlogn(4,1.5,.6).n()
0.424846794957399

For example: https://en.wikipedia.org/wiki/Log-nor...

Then at the moment you need to create your function in mathematical terms. Please see and rate my answer.

Or before. I also cannot confirm with 7.2.beta2

qepcad did install here on 6.10.p1 after I set my MAKE to make -j1.

Sage uses the mpfr library to compute pi to arbitrary precision. The mpfr algorithm apparently has a limit of 646456992 digits. Please refer to

https://github.com/epowers/mpfr/blob/...

Not sure if that is up-to-date, however.

Use simplify_full:

sage: f(x) = sum(k,k,0,x)
sage: f
x |--> 1/2*x^2 + 1/2*x
sage: f(x) = sum(binomial(10,k),k, 0,x)
sage: f
x |--> sum(binomial(10, k), k, 0, x)
sage: f(2)
sum(binomial(10, k), k, 0, 2)
sage: f(2).simplify_full()
56

That's a bug that already has a fix which just needs to be reviewed: http://trac.sagemath.org/ticket/9424

Your proj is ab.dot_product(n)/n.norm()^2*n so your tt*n.norm() is ab.dot_product(n)/n.norm()^2 * n.norm() which is different from proj.norm() because the norm() in tt*n.norm() only applies to n. You made the same mistake when you equaled (tt*n.norm()).simplify_rational() and tt*n.norm().simplify_rational(). Here in the latter the simplify_rational() only applies to n.norm().

Operator precedence in Sage closely follows the same in Python (but in C++ for example the dot would have behaved the same way).

This is right.Multivariate Laurent series are not implemented in Sage at the moment.

A fix should be possible with pynac-0.4.x (pynac is part of Sage); pynac git master already does sqrt(x^2) --> x for x>0 as side effect of other changes.

The y:z can be deduced from the other two, but I have no idea how the results come up specifically.

Miguel, note that sqrt(x^2) != x for x<0.

Maybe http://trac.sagemath.org/ticket/17494 is related. In any case the output of get_memory_usage() increases too.

I confirm the steady increase. This is not reduced by gc.collect(). Maybe it is a Singular issue (Singular is used by Sage in case of multivariate polynomials).

The result consists of two lists: [{x: z}, {x: y}] and [1, 1]. Each list is a possible result that solves the equation. The first list is a Python dictionary (which by definition has no order but gives the values that specific variables will need to satisfy the equation); the second is a list (which simply gives the needed values for the variables in the order the vars were given as argument. Substitution confirms:

sage: P.subs(x==z)
0 == 0
sage: P.subs(x==y)
0 == 0
sage: P.subs(x==1,y==1)
0 == 0

First, with the newest versions of Sage the domain you create a variable with is propagated to the assumption database so you can say:

var('R r L omega k s', domain='real')

I am not sure how you get to the output you give, I got:

sage: Z(s,L) = s * L
sage: Z.diff(s)
(s, L) |--> L
sage: Z
(s, L) |--> L*s
sage: Z(R,r,L,k,omega,s) = R + I * omega * L + ((s * omega**2 * L**2 * k**2) * (r - I * omega * L)) / (r**2 + omega**2 * s **2 * L**2)
sage: Z.diff(s)
(R, r, L, k, omega, s) |--> -2*(-I*L*omega + r)*L^4*k^2*omega^4*s^2/(L^2*omega^2*s^2 + r^2)^2 + (-I*L*omega + r)*L^2*k^2*omega^2/(L^2*omega^2*s^2 + r^2)
sage: Z
(R, r, L, k, omega, s) |--> (-I*L*omega + r)*L^2*k^2*omega^2*s/(L^2*omega^2*s^2 + r^2) + I*L*omega + R

Also, you say that the derivative should be zero. But that's only the case if s is a constant, no?

This is defined behaviour of the general inverse, as far as I understand from the code. For example,

 sage: parent(~1)
 Rational Field

The definition of Matrix_generic_dense.__invert__() explicitly states

Return this inverse of this matrix, as a matrix over the fraction field.

sage: R.fraction_field()
Fraction Field of Univariate Polynomial Ring in t over Integer Ring

I'm not an algebraist so no comment on that but, with symbolics you would stay in the ring, so symbolics seems to be good for something, contrary to many a belief.

sage: mat = matrix([[x^2]])
sage: mati = mat.inverse(); mati
[x^(-2)]
sage: mati[0,0].parent()
Symbolic Ring