How to enter a long logical expression into Wolfram|Alpha?

Questions
1

When I enter an logical expression e.g.

( P && Q && R ) || ( Q && R && S )

I get lots of lovely info. However, I’ve discovered there is a limit to the length of input e.g.

( P && Q && R && S ) || ( P && Q && R && ~S ) || ( P && Q && ~R && S ) || ( P && Q && ~R && ~S ) || ( P && ~Q && R && S ) || ( P && ~Q && R && ~S ) || ( P && ~Q && ~R && S ) || ( P && ~Q && ~R && ~S )

results in a failure message, “Input Too Long! Upload as data using Data input first.”

When I try the data input route, I get another failure message, "“No structured data detected; performing a textual analysis instead.”

How do I structure or otherwise mark my input as being a single logical expression?

2

Inputing an expression as data can’t be used as a way around the maximimum input length in this case. Wolfram|Alpha will interpret anything given as data to be a dataset or a piece of text.

You may want to suggest to the WolframAlpha team that they support boolean expressions as a data format in the future so that you can work with larger boolean expressions than the input bar can handle.

3

Hoping that WolframAlpha will interpret precedence when I eliminate parens and white space I try each of the following

Simplify[P&&Q&&R&&S||P&&Q&&R&&~S||P&&Q&&~R&&S||P&&Q&&~R&&~S||P&&~Q&&R&&S||P&&~Q&&R&&~S]

Simplify[P&&Q&&R&&S||P&&Q&&R&&~S||P&&Q&&~R&&S||P&&Q&&~R&&~S||P&&~Q&&R&&S||P&&~Q&&R&&~S||P&&~Q&&~R&&S]

It happily allows me to enter both within the available line length, understands and correctly interprets the first and cannot comprehend the second.

Thus I presume there is more than one internal limit on the length of input and they do not appear to be consistent.

4

For what it’s worth, Simplify (or LogicalExpand) does the trick and returns P.

Simplify[P&&Q&&R&&S||P&&Q&&R&&!S||P&&Q&&!R&&S||P&&Q&&!R&&!S||P&&!Q&&R&&S||P&&!Q&&R&&!S||P&&!Q&&!R&&S||P&&!Q&&!R&&!S]

P
5

It has been a year and i do not think they have fixed it. I subscribed to the pro version thinking that inputting data through files would fix the issue but it has not :frowning: I am trying to calculate this.
078435243638422372447672231234716695757593735449641234358462086700559213667152171913^733286178582569088283232046829710496185570977121081786863578840329631292141076523731373 mod1026650243044648666338779501960308972649317942706523177961403694692749456133768845419907

for an assignment and sadly it does not work. any suggetions on what i can do?

6

Raphael, Wolfram|Alpha can’t solve that kind of question. Even Mathematica would struggle to do it - your expression would take a ludicrous amount of time to compute. Probably on the order of days.

The exponentiation alone is:

http://www.wolframalpha.com/input/?i=078435243638422372447672231234716695757593735449641234358462086700559213667152171913^733286178582569088283

60785399379915432324698 digits in length.

That alone would take long enough to compute, but you’re expecting a modulus operation on top of that?

It’s just not possible. You would need a supercomputer to calculate that result in anything resembling a “quick” time frame.

7

I don’t think Mathematica struggles that much

In[2]:= AbsoluteTiming[
 PowerMod[078435243638422372447672231234716695757593735449641234358462086700559213667152171913, 73328617858256908828323, 
  1026650243044648666338779501960308972649317942706523177961403694692749456133768845419907]]

Out[2]= {0.000076, 488852248312393495853898207472820633208110722640160160319617509136528516001303946959159}