A composition for a thermoplastic material comprising: - 0 to 70 % by weight, preferably 20 to 60 % by weight, of short reinforcing fibers having a length of between 200 and 400 μm, - 30 to 100 % by weight, preferably 40 to 80 % by weight, of a thermoplastic matrix based on at least one semi-crystalline polyamide polymer, - 0 to 50 % of additives and/or other polymers, where said composition is: a) a reactive composition comprising or consisting of at least one reactive precursor polyamide prepolymer of said semi-crystalline polyamide polymer, or as an alternative to a), b) a non-reactive composition of at least one polyamide polymer, said composition being that of said thermoplastic matrix defined above, and said reactive polyamide prepolymer of composition a) and said polyamide polymer of composition b) comprising or consisting of at least one BACT/XT copolyamide wherein: - BACT is a unit with an amide unit present at a molar content ranging from more than 70 to 99.1 %, preferably from 80 to 99 %, more preferably from 90 to 99 %, where BAC is chosen from 1,3-bis(aminomethyl)cyclohexyl (1,3-BAC), 1,4-bis(aminomethyl)cyclohexyl (1,4-BAC) and a mixture thereof, and T is terephthalic acid, - XT is a unit with an amide unit present at a molar content ranging from 0.9 to less than 30 %, preferably from 1 to 20 %, more preferably from 1 to 10 %, where X is a C9 to C18 linear aliphatic diamine, preferably C9, C10, C11 and C12, and where T is terephthalic acid, preferably C10, C11 or C12. - in the BACT and/or XT units, independently of each other, up to 30 mol%, preferably 20 mol%, particularly up to 10 mol% of terephthalic acid, relative to the total quantity of carboxylic diacids, can be replaced by other aromatic, aliphatic or cycloaliphatic carboxylic diacids comprising 6 to 36 carbon atoms, particularly 6 to 14 carbon atoms, and - in the BACT and/or XT units, independently of each other, up to 30 mol%, preferably 20 mol%, particularly up to 10 mol%, of BAC and/or if applicable X, relative to the total quantity of the diamines, can be replaced by other diamines comprising from 4 to 36 carbon atoms, particularly 6 to 12 carbon atoms, and - in the copolyamide, not more than 30 mol%, preferably not more than 20 %, preferably not more than 10 mol%, relative to the total quantity of the monomers, can be formed by lactams or aminocarboxylic acids, and - provided that the sum of the monomers that replace terephthalic acid, BAC and X does not exceed a concentration of 30 mol%, preferably 20 mol%, preferably 10 mol%, relative to the total quantity of the monomers used in the copolyamide, and - provided that BACT and XT units are still present in said polyamide polymer. - 0 to 70 % by weight, preferably 20 to 60 % by weight, of short reinforcing fibers having a length of between 200 and 400 μm, - 30 to 100 % by weight, preferably 40 to 80 % by weight, of a thermoplastic matrix based on at least one semi-crystalline polyamide polymer, - 0 to 50 % of additives and/or other polymers, a) a reactive composition comprising or consisting of at least one reactive precursor polyamide prepolymer of said semi-crystalline polyamide polymer, or as an alternative to a), b) a non-reactive composition of at least one polyamide polymer, said composition being that of said thermoplastic matrix defined above, - BACT is a unit with an amide unit present at a molar content ranging from more than 70 to 99.1 %, preferably from 80 to 99 %, more preferably from 90 to 99 %, where BAC is chosen from 1,3-bis(aminomethyl)cyclohexyl (1,3-BAC), 1,4-bis(aminomethyl)cyclohexyl (1,4-BAC) and a mixture thereof, and T is terephthalic acid, - XT is a unit with an amide unit present at a molar content ranging from 0.9 to less than 30 %, preferably from 1 to 20 %, more preferably from 1 to 10 %, where X is a C9 to C18 linear aliphatic diamine, preferably C9, C10, C11 and C12, and where T is terephthalic acid, preferably C10, C11 or C12. - in the BACT and/or XT units, independently of each other, up to 30 mol%, preferably 20 mol%, particularly up to 10 mol% of terephthalic acid, relative to the total quantity of carboxylic diacids, can be replaced by other aromatic, aliphatic or cycloaliphatic carboxylic diacids comprising 6 to 36 carbon atoms, particularly 6 to 14 carbon atoms, and - in the BACT and/or XT units, independently of each other, up to 30 mol%, preferably 20 mol%, particularly up to 10 mol%, of BAC and/or if applicable X, relative to the total quantity of the diamines, can be replaced by other diamines comprising from 4 to 36 carbon atoms, particularly 6 to 12 carbon atoms, and - in the copolyamide, not more than 30 mol%, preferably not more than 20 %, preferably not more than 10 mol%, relative to the total quantity of the monomers, can be formed by lactams or aminocarboxylic acids, and - provided that the sum of the monomers that replace terephthalic acid, BAC and X does not exceed a concentration of 30 mol%, preferably 20 mol%, preferably 10 mol%, relative to the total quantity of the monomers used in the copolyamide, and - provided that BACT and XT units are still present in said polyamide polymer.