An interpolymer is prepared from a polymerizable olefinically unsaturated carboxylic acid containing at least one activated carbon-to-carbon double bond and at least one carboxyl group, and a polyalkenyl polyether of a polyhydric alcohol, the polyether containing more than one alkenyl ether grouping per molecule, and the parent polyhydric alcohol containing at least four carbon atoms to which are attached at least three hydroxyl groups.  The acid may be acrylic, methacrylic, ethacrylic, a -chloro-, a -cyano, a -bromo, a -phenyl-, a -benzyl- or a -cyclohexyl-acrylic, crotonic, b -acryloxy-propionic, hydrosorbic, sorbic, a -chloro sorbic, a -butyl crotonic, angelic, cinnamic, m-chloro cinnamic, p-chloro cinnamic, umbellic, b -styryl acrylic, maleic, fumaric, hydromuconic, glutaconic, itaconic, citraconic, mesaconic, muconic, aconitic, tri- and tetra-carboxy ethylene, b -acryloxy acrylic, 3-carboxy-pentadiene-(2,4)-oic-1 or there may be used maleic anhydride or an anhydride substitution product thereof.  The polyhydric alcohol from which the polyalkenyl polyether is prepared may be 1,2,3-butane triol, 2,3,4-trihydroxy butyric acid, erythrose, threose, erythrulose, arabinose, xylose, lyxose, ribose, araboketose, xyloketose, glucose, galactose, mannose, gulose, idose, talose, allose, fructose, sorbose, sucrose, maltose, lactose, raffinose, a hexosan, pentosan or hexosan-pentosan, a galactomannan or glucomannan gum, starch, erythritol, xylitol, mono-, di-, or tri-pentaerythritol, arabitol, mannitol, iditol, tolitol, sorbitol, inositol, dulcitol, gluconic, glucuronic, galactonic, galacturonic, saccharic, mucic or pectic acid.  The alkenyl group of the polyalkenyl polyether may be vinyl, allyl or crotyl.  Additional monomers which may be incorporated in the monomer mixture are styrene, the chloro- and ethoxy-styrenes, acrylamide, methacrylamide, N-methyl acrylamide, N,N-dimethyl acrylamide, acrylonitrile, methacrylonitrile, methyl and ethyl acrylate, 2-ethyl-hexyl acrylate, methyl methacrylate, vinyl acetate, vinyl benzoate, vinyl pyridine, vinyl chloride, vinylidene chloride, vinylidene chlorobromide, vinyl carbazole, vinyl pyrrolidone, methyl, ethyl and n-butyl vinyl ether, methyl vinyl ketone, ethylene, isobutylene, dimethyl and diethyl maleate, divinyl ether, diallyl maleate, ethylene glycol dimethacrylate, acrylic anhydride and b -allyloxy-acrylate.  Preferred interpolymers are those prepared from monomer mixtures containing acrylic acid or maleic anhydride and allyl sucrose. Polymerization is preferably effected in a solvent for the monomers, which is a non-solvent for the polymer, or a mixture of such solvents, suitable solvents being benzene, xylene, hexane, heptane, carbon tetrachloride, methyl chloride, ethyl chloride and bromotrichloro-methane.  Polymerization may also be effected in aqueous medium when the copolymers may be obtained as a granular precipitate or as a highly swollen gel. Suitable polymerization catalysts are sodium, potassium and ammonium persulphates, caprylyl, benzoyl, hydrogen and pelargonyl peroxides, cumene hydroperoxide, tertiary butyl diperphthalate and perbenzoate, sodium peracetate and percarbonate and azo diisobutyryl nitrile. Redox and heavy-metal activated catalyst systems may also be used. The polymers are useful as cation-exchange resins in their as-obtained acid condition and as anion-exchange resins when converted to alkali metal, ammonium or amine salts.  A composition suitable for use as a toothpaste comprises 25 parts of sodium metaphosphate, 25 parts of calcium hydrogen phosphate, 50 parts of 40 per cent aqueous glycerol, 2 parts of a sodium sulphate or sulphonate and 1.5 parts of 75 per cent sodium salt of a copolymer of acrylic acid and allyl sucrose.  A car or furniture cleaner comprises a copolymer of maleic anhydride, vinyl methyl ether and allyl sucrose modified by half-ester formation or by partial amine-amide salt formation, scouring agents such as fine pumice and diatomaceous earth, and polishing agents such as oily hydrocarbons, vegetable oils and waxes.ALSO:Poly-alkenyl ethers are produced by reacting an alkenyl halide, or a mixture of such halides, such as allyl chloride or bromide and methallyl chloride or bromide with a strongly alkaline aqueous solution of one or more polyhydric alcohols containing at least 4 carbon atoms and at least 3 hydroxyl groups.  Polyhydric alcohols specified are 1,2,3-butane triol, 2,3,4-trihydroxy butyric acid, erythrose, threose, erythulose, arabinose, xylose, lyxose, ribose, araboketose, xyloketose, glycose, galactose, mannose, gulose, idose, talose, allose, fructose, sorbose, sucrose, maltose, lactose, raffinose, a hexosan, pentosan or hexosanpentosan, a galactomannan or glucomannan gum, starch, erythritol, xylitol, mono-, di- and tri-pentaerythritol, arabitol, mannitol, iditol, talitol, sorbitol, inositol, dulcitol, gluconic acid, glucuronic acid, galactonic, galacturonic, saccharic, mucic or pectic acid.  The preparation of a polyallyl polyether of sucrose is described.ALSO:Toothpaste comprises 25 parts of sodium metaphosphate, 25 parts of calcium hydrogen phosphate, 50 parts of 40 per cent aqueous glycerol, 2 parts of a sodium sulphate or sulphonate and 1.5 parts of 75 per cent sodium salt of a copolymer of acrylic acid and alkyl sucrose.