The synthetic division operator is looks like a floor symbol. But it is not exactly floor symbol. I tried a lot to find out the synthetic division operator using detexify. But I didn't find out it. How can I write synthetic division using MathJax?
I found this website: https://mathhelpboards.com/threads/synthetic-and-polynomial-long-division.10218/
It says that you can use this code:
\begin{array}{c|rrr}&1&2&1\\-1&&-1&-1\\\hline\\&1&1&0\\\end{array}
And I'm sure you can find a way to replace the numbers to fit your liking.
Related
Implement a data type to represent "large numbers" and operate with them. A "large number" is an integer that can have up to 200 digits. For internal representation of numbers will use strings. On these numbers are defined arithmetic operations (operators +, -, *), relational (>, <, = =, etc.). Build a program that exemplifies the usage of such numbers.
Basically they are asking you to create your own implementation of BigInteger
https://docs.oracle.com/javase/7/docs/api/java/math/BigInteger.html
Which represents VERY large numbers using Strings to avoid the limitations of binary represented numbers. Math is performed on them using the digits directly similar to how you might do it using a pencil and paper.
I am communicating with a servo using python's serial module. When I perform a serial.read(1) I get the value '\x80'. I need to convert this to decimal (128). Any suggestions?
Oh, never mind. I should have thought a bit. Googling opposite of chr() found me this page in the python docs. And ord() does the trick.
I am trying to make basic constructions like "get intersection of a line and circle", "connect two points", "create a circle" with CGAL. However, the choice of kernel seems to be a problem. When I use exact 2D circular kernel, I get Circular_arc_point_2 from intersections, and then I can't use this data type to create lines, circles; and converting to Point_2 seems to introduce error and then stores the approximate value as an exact number. Additionally this problem seems to be independent of the choice of kernel.
What is a proper way of those constructions? Exact and approximate number are all fine as long as the data type is consistent in these constructions.
In the worst case, if this is unresolvable, is there any other free library with this functionality?
The predefined Exact_circular_kernel_2 only uses rational number as its field type. To cover every constructible point, you should define a circular kernel that uses a FieldWithSqrt. With existing types and traits it is simple:
using L = CGAL::Exact_predicates_exact_constructions_kernel_with_sqrt;
using A = CGAL::Algebraic_kernel_for_circles_2_2<L::FT>;
using K = CGAL::Circular_kernel_2<L, A>;
Then you can convert a Circular_arc_point_2 p to Point_2 with the exact coordinates:
K::Point_2 q(p.x(), p.y());
Circular_arc_point_2 is a point which coordinates are algebraic numbers of degree 2 (only way to represent exactly the intersection of 2 circles). You can convert the point into regular floating point coordinate Point_2 by using for example Point_2(to_double(cp.x()), to_double(cp.y())) but then you'll be loosing the exactness.
I'm working on a NodeJs script that handles strings with exponential values.
Something like this:
1.070000000000000e+003
Which is the best way to convert (or parse) this string and obtain a floating value?
Thanks for the help.
You may convert by using parseFloat or Number
If you prefer to parse, maybe the best way is by a regular expression:
/-?(?:0|[1-9]\d*)(?:\.\d*)?(?:[eE][+\-]?\d+)?/
as suggested here and convert the single capturing group.
I am working on a project, which is based on optix. I need to use progressive photon mapping, hence I am trying to use the Progressive Photon Mapping from the samples, but the transparency material is not implemented.
I've googled a lot and also tried to understand other samples that contains transparency material (e.g. Glass, Tutorial, whitted). At last, I got the solution as follows;
Find the hit point (intersection point) (h below)
Generate another ray from that point
use the color of the new generated points
By following you can also find the code of that part, by I do not understand why I get black color(.0f, .0f, 0.f) for the new generated ray (part 3 above).
optix::Ray ray( h, t, rtpass_ray_type, scene_epsilon );
HitPRD refr_prd;
refr_prd.ray_depth = hit_prd.ray_depth+1;
refr_prd.importance = importance;
rtTrace( top_object, ray, refr_prd );
result += (1.0f - reflection) * refraction_color * refr_prd.attenuation;
Any idea will be appreciated.
Please note that refr_prd.attenuation should contains some colors, after using function rtTrace(). I've mentioned reflection and reflaction_color to help you better understand the procedure. You can simply ignore them.
There are a number of methods to diagnose your problem.
Isolate the contribution of the refracted ray, by removing any contribution of the reflection ray.
Make sure you have a miss program. HitPRD::attenuation needs to be written to by all of your closest hit programs and your miss programs. If you suspect the miss program is being called set your miss color to something obviously bad ([1,0,1] is my favorite).
Use rtPrintf in combination with rtContextSetPrintLaunchIndex or setPrintLaunchIndex to print out the individual values of the product to see which term is zero from a given pixel. If you don't restrict the output to a given launch index you will get too much output. You probably also want to print out the depth as well.