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Knowledge of lectin and glycosidase specificities is fundamental to the study of glycobiology. The primary specificities of such molecules can be uncovered using well-established tools, but the complex details of their specificities are difficult to determine and describe. Here we present a language and algorithm for the analysis and description of glycan motifs with high complexity. The language uses human-readable notation and wildcards, modifiers, and logical operators to define motifs of nearly any complexity. By applying the syntax to the analysis of glycan-array data, we found that the lectin AAL had higher binding where fucose groups are displayed on separate branches. The lectin SNA showed gradations in binding based on the length of the extension displaying sialic acid and on characteristics of the opposing branches. A new algorithm to evaluate changes in lectin binding upon treatment with exoglycosidases identified the primary specificities and potential fine specificities of an α1-2-fucosidase and an α2-3,6,8-neuraminidase. The fucosidase had significantly lower action where sialic acid neighbors the fucose, and the neuraminidase showed statistically lower action where α1-2 fucose neighbors the sialic acid or is on the opposing branch. The complex features identified here would have been inaccessible to analysis using previous methods. The new language and algorithms promise to facilitate the precise determination and description of lectin and glycosidase specificities.