? tst12([all,all],[a,b,c,d,x,y],eq,"y<(x+a)^15+b,y<(x+c)^15+d");Ans(1);
*** using Lazard's method (MPP17).
[y,2]
[x,1]
[d,4]
[c,7]
[b]
[a,1]
time = 1min, 36,784 ms.
3 3(0,0) 37(84,7) 535(26,54) 1647(52,12) 9(0,6)
*** combined adjacent 8 cells.
1[true,true,c = [a-c,1],d = [b-d,1],true,true]
time = 9,594 ms.
Wolfram Language 12.3.0 Engine for Linux x86 (64-bit)
Copyright 1988-2021 Wolfram Research, Inc.
In[1]:= Reduce[ForAll[{x,y},Equivalent[y<(x+a)^5+b,y<(x+c)^5+d]],{a,b,c,d},Reals,WorkingPrecision->30]//Timing
Out[1]= {0.104536, c == a && d == a^5 + b - c^5}
In[2]:= Reduce[ForAll[{x,y},Equivalent[y<(x+a)^6+b,y<(x+c)^6+d]],{a,b,c,d},Reals,WorkingPrecision->30]//Timing
Out[2]= {0.476967, c == a && d == a^6 + b - c^6}
In[3]:= Reduce[ForAll[{x,y},Equivalent[y<(x+a)^7+b,y<(x+c)^7+d]],{a,b,c,d},Reals,WorkingPrecision->30]//Timing
Out[3]=
{0.528524, (a < 0 && c == a && d == a^7 + b - c^7) || (a == 0 && c == 0 && d == b) ||
(a > 0 && c == a && d == a^7 + b - c^7)}
In[4]:= Reduce[ForAll[{x,y},Equivalent[y<(x+a)^8+b,y<(x+c)^8+d]],{a,b,c,d},Reals,WorkingPrecision->30]//Timing
Out[4]= {36.708199, c == a && d == a^8 + b - c^8}
In[5]:= Reduce[ForAll[{x,y},Equivalent[y<(x+a)^9+b,y<(x+c)^9+d]],{a,b,c,d},Reals,WorkingPrecision->30]//Timing
Out[5]= {4.41101, c == a && d == a^9 + b - c^9}
In[6]:= Reduce[ForAll[{x,y},Equivalent[y<(x+a)^10+b,y<(x+c)^10+d]],{a,b,c,d},Reals,WorkingPrecision->30]//Timing
Out[6]= {368.027142, c == a && d == a^10 + b - c^10}
In[7]:= Reduce[ForAll[{x,y},Equivalent[y<(x+a)^11+b,y<(x+c)^11+d]],{a,b,c,d},Reals,WorkingPrecision->30]//Timing
Reduce::cadpr: The cylindrical algebraic decomposition algorithm used by Reduce
failed due to a too low WorkingPrecision. Increasing the value of WorkingPrecision may allow the algorithm
to succeed.
^C
Interrupt> a
Out[7]= $Aborted
In[8]:= Reduce[ForAll[{x,y},Equivalent[y<(x+a)^11+b,y<(x+c)^11+d]],{a,b,c,d},Reals,WorkingPrecision->60]//Timing
Out[8]= {27.447685, c == a && d == a^11 + b - c^11}
