Some first steps towards discovering what this error means. A most useful tool here is a debugger as it allows you to stop at the condition generating this error message in line 21 of **RegularChains:-TRDisolate_real_zeros** (see ?debugger , or try mdcs ), as shown here:

showstat(RegularChains::TRDisolate_real_zeros,21..22);
RegularChains:-TRDisolate_real_zeros := proc(real_point, p_list, R)
local vars, n, lower_rc, lower_cube, p, index_list, interval_list, interval_element, i, inner_real_point, k, rc, mycube, mybox;
...
21 if nops(interval_list) <> nops(index_list) then
22 error "error in TRDisolate_real_zeros in univariate case"
end if;
...
end proc

And the exception is triggered as the number of operands of these two lists are different. Their evaluation yields this output (in mdcs):

(**) interval_list
[[[0, 0]], [[6231/65536, 12465/131072]], [[12471/131072, 6237/65536]],
[[105/1024, 27/256]], [[39/128, 81/256]], [[21/64, 87/256]], [[15/16, 33/32]],
[[15/16, 33/32]], [[87/64, 45/32]], [[87/64, 45/32]], [[363/256, 183/128]],
[[369/256, 93/64]], [[189/128, 1515/1024]]]
(**)index_list
[7, 3, 4, 5, 5, 4, 4, 4, 6, 4]

So, the next step is finding why these two lists have different number of operands. Look at the conditional statement starting at line 11:

11 if nops(p_list) = 1 then
12 index_list := [seq(1,i = 1 .. nops(interval_list))]
else
13 rc := TRDpretend_regular_chain(p,TRDempty_regular_chain(),R);
14 for interval_element in interval_list do
15 mycube := interval_element;
16 mybox := TRDconvert_cad_sample_to_box([rc, mycube],R);
17 for i to nops(p_list) do
18 if TRDsign_poly_at_box(p_list[i],mybox,R) = 0 then
19 index_list := [op(index_list), i];
20 break
end if
end do
end do
end if;

Here, **p_list** is a parameter, and evaluates as a list with 7 operands:

(**) p_list
[beta+1,
beta^20-beta^19-10*beta^18+10*beta^17+45*beta^16-45*beta^15-120*beta^14+120*beta
^13+210*beta^12-210*beta^11-252*beta^10+252*beta^9+210*beta^8-210*beta^7-120*
beta^6+120*beta^5+45*beta^4-45*beta^3-10*beta^2+10*beta+1,
beta^22-11*beta^20+55*beta^18-165*beta^16+330*beta^14-462*beta^12+462*beta^10-
330*beta^8+165*beta^6-55*beta^4+11*beta^2+beta-1,
beta^38-beta^37-19*beta^36+19*beta^35+171*beta^34-171*beta^33-969*beta^32+969*
beta^31+3876*beta^30-3876*beta^29-11628*beta^28+11628*beta^27+27132*beta^26-
27132*beta^25-50388*beta^24+50388*beta^23+75582*beta^22-75582*beta^21-92379*beta
^20+92377*beta^19+92388*beta^18-92368*beta^17-75627*beta^16+75537*beta^15+50508*
beta^14-50268*beta^13-27342*beta^12+26922*beta^11+11880*beta^10-11376*beta^9-
4086*beta^8+3666*beta^7+1089*beta^6-849*beta^5-216*beta^4+126*beta^3+29*beta^2-9
*beta-1, beta-1,
beta^18-beta^17-9*beta^16+9*beta^15+36*beta^14-36*beta^13-84*beta^12+84*beta^11+
126*beta^10-126*beta^9-126*beta^8+126*beta^7+84*beta^6-84*beta^5-36*beta^4+36*
beta^3+9*beta^2-9*beta-1, beta]

so that the computation follows the **else** part. Then, some leads to follow are: 1. what happens in this part, and 2. why **p_list** gets this value.