| 共形几何代数中的分阶幂零单项式的几何解释 |
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| 引用本文： | 李洪波.共形几何代数中的分阶幂零单项式的几何解释[J].中国科学:数学,2021(1). |
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| 作者姓名： | 李洪波 |
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| 作者单位： | 中国科学院数学与系统科学研究院;中国科学院大学数学科学学院 |
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| 基金项目： | 国家自然科学基金(批准号:11671388)资助项目。 |
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| 摘 要： | 本文进一步发展共形几何代数,从代数和几何两个角度对共形几何代数中由幂零向量生成的分阶单项式的代数性质和几何解释进行深入探讨,包括各种维数的球面和平面定向的代数刻画、长括号的三角学、角度和方向的幂零单项式分阶表示、幂零单项式各个分阶的几何意义等.这些结果有助于理解高层次符号代数运算背后的几何意义,以及共形几何代数简化符号几何计算的内在机制.
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| 关 键 词： | 共形几何代数 符号几何计算 三角学 零括号代数 几何约束的代数表达 |
Geometric interpretations of graded null monomials in conformal geometric algebra |
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| Hongbo Li.Geometric interpretations of graded null monomials in conformal geometric algebra[J].Scientia Sinica Mathemation,2021(1). |
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| Authors: | Hongbo Li |
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| Abstract: | This paper further develops conformal geometric algebra(CGA)from both the algebraic aspect and the geometric viewpoint,by exploring the algebraic properties and geometric interpretations of the graded monomials generated by null vectors.The content includes the computation of the orientations of various dimensional spheres and planes,the trigonometry of long brackets,the graded null monomial representation of angles and directions,the geometric meaning of various single-graded null monomials,etc.These results help not only in understanding the geometric implication of various advanced symbolic algebraic manipulations in conformal geometric algebra,but also in clarifying the intrinsic machinery behind the efficiency brought about by conformal geometric algebra in symbolic geometric computing. |
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| Keywords: | conformal geometric algebra symbolic geometric computation trigonometry null bracket al-gebra algebraic expressions of geometric constraints |
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