@conn96 Please type your question here, and do not use images.

The result in Maple 16 is

I see the significant difference. In M17, the first coordinate becomes the parameter. I agree that the M16 way is better.

The result in Maple 16 is

I see the significant difference. In M17, the first coordinate becomes the parameter. I agree that the M16 way is better.

Your statement in quotes is ungrammatical in mathematical English. I don't often criticize grammar, but in this case there are many different interpretations possible depending on how quantifiers are placed in the statement. Quantifiers are phrases such as "for all", "for every", "there exists", "there is", etc.

One possible interpretation is "I want to find conditions on a, b, c, d such that whenever A, B, C are three points with integer coordinates on the curve y = (a*x+b)/(c*x+d), then the centroid of ABC also has integer coordinates and is also on the curve".

Another is "I want to find constants a, b, c, d such that there exists a triangle ABC with centroid O such that all four points have integer coordinates and all are on the curve y = (a*x+b)/(c*x+d)".

And there are many others. Perhaps you'd be better off expressing the statement in symbols.

Would you please provide the exact sequence of commands, or an example of a sequence of commands, that behaves differently?

You can reduce the number of significant digits displayed for individual results by using evalf[n](...) where n is the number of digits desired. For example,

evalf(Pi);
                        3.14159265358979
evalf[5](%);
                             3.1416

You can reduce the number of significant digits displayed for individual results by using evalf[n](...) where n is the number of digits desired. For example,

evalf(Pi);
                        3.14159265358979
evalf[5](%);
                             3.1416

About 3/4 of the entries in your sequence have nonzero imaginary part. How do you want to handle that?

There is a difference between the computational precision and the display precision. The computational precision is controlled by the Digits environment variable. The display precision is controlled by interface(displayprecision= ...). Unfortunately, the display precision is measured as number of digits after the decimal point rather than as number of significant digits. 

There is a difference between the computational precision and the display precision. The computational precision is controlled by the Digits environment variable. The display precision is controlled by interface(displayprecision= ...). Unfortunately, the display precision is measured as number of digits after the decimal point rather than as number of significant digits. 

@Alex Joannou You should probably make a separate question. Replies to Answers do not make a thread come to the top of the Active Conversations queue, which makes it difficult to follow the thread. Also, Replies are not searchable AFAIK.

Can you show an example of what you mean by partitioning an integer into sets? By example, I mean Can you take a small integer n and list here all the structures that you want to count? It's possible that you want to count Compositions rather than Partitions.

@Alex Joannou You should probably make a separate question. Replies to Answers do not make a thread come to the top of the Active Conversations queue, which makes it difficult to follow the thread. Also, Replies are not searchable AFAIK.

Can you show an example of what you mean by partitioning an integer into sets? By example, I mean Can you take a small integer n and list here all the structures that you want to count? It's possible that you want to count Compositions rather than Partitions.

with(combstruct);
count(Partition(10));
allstructs(Partition(10));

See ?combstruct,structures .

with(combstruct);
count(Partition(10));
allstructs(Partition(10));

See ?combstruct,structures .

@casperyc Your two-stage method and my two-stage method may be effectively the same thing. Either way, it's much much better timewise than passing all the polynomial substitutions to simplify at the same time.