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Using Macaulay2 from within R : the m2r package Christopher ONeill University of California Davis coneill@math.ucdavis.edu Joint with David Kahle and Jeff Sommars Mathematics Research Communities on Algebraic Statistics August 3, 2017

  1. Under the hood: sockets wait for input from client m2("1+1") send "1+1" to server wait for response receive "1+1" from client evaluate "1+1" to "2" send "2" to client Christopher O’Neill (UC Davis) The m2r package August 3, 2017 6 / 20

  2. Under the hood: sockets wait for input from client m2("1+1") send "1+1" to server wait for response receive "1+1" from client evaluate "1+1" to "2" send "2" to client wait for input from client Christopher O’Neill (UC Davis) The m2r package August 3, 2017 6 / 20

  3. Under the hood: sockets wait for input from client m2("1+1") send "1+1" to server wait for response receive "1+1" from client evaluate "1+1" to "2" send "2" to client wait for input from client receive "2" from server Christopher O’Neill (UC Davis) The m2r package August 3, 2017 6 / 20

  4. Under the hood: sockets wait for input from client m2("1+1") send "1+1" to server wait for response receive "1+1" from client evaluate "1+1" to "2" send "2" to client wait for input from client receive "2" from server return "2" from m2() Christopher O’Neill (UC Davis) The m2r package August 3, 2017 6 / 20

  5. Under the hood: sockets Christopher O’Neill (UC Davis) The m2r package August 3, 2017 7 / 20

  6. Under the hood: sockets > Christopher O’Neill (UC Davis) The m2r package August 3, 2017 7 / 20

  7. Under the hood: sockets > m2("a = 5") [1] "5" > m2("a") [1] "5" > Christopher O’Neill (UC Davis) The m2r package August 3, 2017 7 / 20

  8. Under the hood: sockets > m2("a = 5") [1] "5" > m2("a") [1] "5" > m2("1+") Error: Macaulay2 Error! > Christopher O’Neill (UC Davis) The m2r package August 3, 2017 7 / 20

  9. Under the hood: sockets > m2("a = 5") [1] "5" > m2("a") [1] "5" > m2("1+") Error: Macaulay2 Error! > m2("2+1") [1] "3" Christopher O’Neill (UC Davis) The m2r package August 3, 2017 7 / 20

  10. Under the hood: sockets > Christopher O’Neill (UC Davis) The m2r package August 3, 2017 8 / 20

  11. Under the hood: sockets > start_m2() Starting M2... done. > m2("1+1") [1] "2" > Christopher O’Neill (UC Davis) The m2r package August 3, 2017 8 / 20

  12. Under the hood: sockets > start_m2() Starting M2... done. > m2("1+1") [1] "2" > So. . . now what? Christopher O’Neill (UC Davis) The m2r package August 3, 2017 8 / 20

  13. Under the hood: sockets > start_m2() Starting M2... done. > m2("1+1") [1] "2" > So. . . now what? New features since creation: Lots of convenience functions High-level parser Cloud computing Christopher O’Neill (UC Davis) The m2r package August 3, 2017 8 / 20

  14. Convenience functions > m2("a = 5") [1] "5" > m2("a") [1] "5" > Christopher O’Neill (UC Davis) The m2r package August 3, 2017 9 / 20

  15. Convenience functions > m2("a = 5") [1] "5" > m2("a") [1] "5" > m2("R = QQ[x,y,z]") [1] "QQ(monoid[x..z, Degrees => {3:1}, Heft => {1}, MonomialOrder => VerticalList{MonomialSize => 32, GRevLex => {3:1}, Position => Up}, DegreeRank => 1])" > Christopher O’Neill (UC Davis) The m2r package August 3, 2017 9 / 20

  16. Convenience functions > m2("a = 5") [1] "5" > m2("a") [1] "5" > m2("R = QQ[x,y,z]") [1] "QQ(monoid[x..z, Degrees => {3:1}, Heft => {1}, MonomialOrder => VerticalList{MonomialSize => 32, GRevLex => {3:1}, Position => Up}, DegreeRank => 1])" > m2("I = ideal(xˆ2, x*y, xˆ3*yˆ2)") [1] "ideal map((R)ˆ1,(R)ˆ{{-2},{-2},{-5}},{{xˆ2, x*y, xˆ3*yˆ2}})" > Christopher O’Neill (UC Davis) The m2r package August 3, 2017 9 / 20

  17. Convenience functions > m2("a = 5") [1] "5" > m2("a") [1] "5" > m2("R = QQ[x,y,z]") [1] "QQ(monoid[x..z, Degrees => {3:1}, Heft => {1}, MonomialOrder => VerticalList{MonomialSize => 32, GRevLex => {3:1}, Position => Up}, DegreeRank => 1])" > m2("I = ideal(xˆ2, x*y, xˆ3*yˆ2)") [1] "ideal map((R)ˆ1,(R)ˆ{{-2},{-2},{-5}},{{xˆ2, x*y, xˆ3*yˆ2}})" > m2("gens gb I") [1] "map((R)ˆ1,(R)ˆ{{-2},{-2}},{{x*y, xˆ2}})" Christopher O’Neill (UC Davis) The m2r package August 3, 2017 9 / 20

  18. Convenience functions > m2("a = 5") [1] "5" > m2("a") [1] "5" > m2("R = QQ[x,y,z]") [1] "QQ(monoid[x..z, Degrees => {3:1}, Heft => {1}, MonomialOrder => VerticalList{MonomialSize => 32, GRevLex => {3:1}, Position => Up}, DegreeRank => 1])" > m2("I = ideal(xˆ2, x*y, xˆ3*yˆ2)") [1] "ideal map((R)ˆ1,(R)ˆ{{-2},{-2},{-5}},{{xˆ2, x*y, xˆ3*yˆ2}})" > m2("gens gb I") [1] "map((R)ˆ1,(R)ˆ{{-2},{-2}},{{x*y, xˆ2}})" Christopher O’Neill (UC Davis) The m2r package August 3, 2017 9 / 20

  19. Convenience functions > m2("a = 5") [1] "5" > m2("a") [1] "5" > Christopher O’Neill (UC Davis) The m2r package August 3, 2017 10 / 20

  20. Convenience functions > m2("a = 5") [1] "5" > m2("a") [1] "5" > (R <- ring("x", "y", "z", coefring = "QQ")) M2 Ring: QQ[x,y,z], grevlex order > Christopher O’Neill (UC Davis) The m2r package August 3, 2017 10 / 20

  21. Convenience functions > m2("a = 5") [1] "5" > m2("a") [1] "5" > (R <- ring("x", "y", "z", coefring = "QQ")) M2 Ring: QQ[x,y,z], grevlex order > (I <- ideal("xˆ2", "x*y", "xˆ3*yˆ2")) M2 Ideal of ring QQ[x,y,z] (grevlex) with generators : < xˆ2, x y, xˆ3 yˆ2 > > Christopher O’Neill (UC Davis) The m2r package August 3, 2017 10 / 20

  22. Convenience functions > m2("a = 5") [1] "5" > m2("a") [1] "5" > (R <- ring("x", "y", "z", coefring = "QQ")) M2 Ring: QQ[x,y,z], grevlex order > (I <- ideal("xˆ2", "x*y", "xˆ3*yˆ2")) M2 Ideal of ring QQ[x,y,z] (grevlex) with generators : < xˆ2, x y, xˆ3 yˆ2 > > (mygens <- gb(I)) x y xˆ2 > Christopher O’Neill (UC Davis) The m2r package August 3, 2017 10 / 20

  23. Convenience functions > m2("a = 5") [1] "5" > m2("a") [1] "5" > (R <- ring("x", "y", "z", coefring = "QQ")) M2 Ring: QQ[x,y,z], grevlex order > (I <- ideal("xˆ2", "x*y", "xˆ3*yˆ2")) M2 Ideal of ring QQ[x,y,z] (grevlex) with generators : < xˆ2, x y, xˆ3 yˆ2 > > (mygens <- gb(I)) x y xˆ2 > mygens[[2]] xˆ2 Christopher O’Neill (UC Davis) The m2r package August 3, 2017 10 / 20

  24. Convenience functions > m2("a = 5") [1] "5" > m2("a") [1] "5" > (R <- ring("x", "y", "z", coefring = "QQ")) M2 Ring: QQ[x,y,z], grevlex order > (I <- ideal("xˆ2", "x*y", "xˆ3*yˆ2")) M2 Ideal of ring QQ[x,y,z] (grevlex) with generators : < xˆ2, x y, xˆ3 yˆ2 > > (mygens <- gb(I)) x y xˆ2 > mygens[[2]] − mpoly ← xˆ2 Christopher O’Neill (UC Davis) The m2r package August 3, 2017 10 / 20

  25. Convenience functions > m2("a = 5") [1] "5" > m2("a") [1] "5" > (R <- ring("x", "y", "z", coefring = "QQ")) M2 Ring: QQ[x,y,z], grevlex order > (I <- ideal("xˆ2", "x*y", "xˆ3*yˆ2")) M2 Ideal of ring QQ[x,y,z] (grevlex) with generators : < xˆ2, x y, xˆ3 yˆ2 > > (mygens <- gb(I)) − mpolylist ← x y xˆ2 > mygens[[2]] − mpoly ← xˆ2 Christopher O’Neill (UC Davis) The m2r package August 3, 2017 10 / 20

  26. Convenience functions > (I <- ideal("xˆ2", "x*y", "xˆ3*yˆ2")) M2 Ideal of ring QQ[x,y,z] (grevlex) with generators : < xˆ2, x y, xˆ3 yˆ2 > > Christopher O’Neill (UC Davis) The m2r package August 3, 2017 11 / 20

  27. Convenience functions > (I <- ideal("xˆ2", "x*y", "xˆ3*yˆ2")) M2 Ideal of ring QQ[x,y,z] (grevlex) with generators : < xˆ2, x y, xˆ3 yˆ2 > > radical(I) M2 Ideal of ring QQ[x,y,z] (grevlex) with generator : < x > > Christopher O’Neill (UC Davis) The m2r package August 3, 2017 11 / 20

  28. Convenience functions > (I <- ideal("xˆ2", "x*y", "xˆ3*yˆ2")) M2 Ideal of ring QQ[x,y,z] (grevlex) with generators : < xˆ2, x y, xˆ3 yˆ2 > > radical(I) M2 Ideal of ring QQ[x,y,z] (grevlex) with generator : < x > > saturate(I,ideal("xˆ5")) M2 Ideal of ring QQ[x,y,z] (grevlex) with generator : < 1 > > Christopher O’Neill (UC Davis) The m2r package August 3, 2017 11 / 20

  29. Convenience functions > (I <- ideal("xˆ2", "x*y", "xˆ3*yˆ2")) M2 Ideal of ring QQ[x,y,z] (grevlex) with generators : < xˆ2, x y, xˆ3 yˆ2 > > radical(I) M2 Ideal of ring QQ[x,y,z] (grevlex) with generator : < x > > saturate(I,ideal("xˆ5")) M2 Ideal of ring QQ[x,y,z] (grevlex) with generator : < 1 > > I+I M2 Ideal of ring QQ[x,y,z] (grevlex) with generators : < xˆ2, x y, xˆ3 yˆ2, xˆ2, x y, xˆ3 yˆ2 > > Christopher O’Neill (UC Davis) The m2r package August 3, 2017 11 / 20

  30. Convenience functions > (I <- ideal("xˆ2", "x*y", "xˆ3*yˆ2")) M2 Ideal of ring QQ[x,y,z] (grevlex) with generators : < xˆ2, x y, xˆ3 yˆ2 > > radical(I) M2 Ideal of ring QQ[x,y,z] (grevlex) with generator : < x > > saturate(I,ideal("xˆ5")) M2 Ideal of ring QQ[x,y,z] (grevlex) with generator : < 1 > > I+I M2 Ideal of ring QQ[x,y,z] (grevlex) with generators : < xˆ2, x y, xˆ3 yˆ2, xˆ2, x y, xˆ3 yˆ2 > > gb(I+I) x y xˆ2 Christopher O’Neill (UC Davis) The m2r package August 3, 2017 11 / 20

  31. Convenience functions > (I <- ideal("xˆ2", "x*y", "xˆ3*yˆ2")) M2 Ideal of ring QQ[x,y,z] (grevlex) with generators : < xˆ2, x y, xˆ3 yˆ2 > > Christopher O’Neill (UC Davis) The m2r package August 3, 2017 12 / 20

  32. Convenience functions > (I <- ideal("xˆ2", "x*y", "xˆ3*yˆ2")) M2 Ideal of ring QQ[x,y,z] (grevlex) with generators : < xˆ2, x y, xˆ3 yˆ2 > > primary_decomposition(I) M2 List of ideals of QQ[x,y,z] (grevlex) : < x > < xˆ2, y > > Christopher O’Neill (UC Davis) The m2r package August 3, 2017 12 / 20

  33. Convenience functions > (I <- ideal("xˆ2", "x*y", "xˆ3*yˆ2")) M2 Ideal of ring QQ[x,y,z] (grevlex) with generators : < xˆ2, x y, xˆ3 yˆ2 > > primary_decomposition(I) M2 List of ideals of QQ[x,y,z] (grevlex) : < x > < xˆ2, y > > dimension(I) [1] 2 > Christopher O’Neill (UC Davis) The m2r package August 3, 2017 12 / 20

  34. Convenience functions > (I <- ideal("xˆ2", "x*y", "xˆ3*yˆ2")) M2 Ideal of ring QQ[x,y,z] (grevlex) with generators : < xˆ2, x y, xˆ3 yˆ2 > > primary_decomposition(I) M2 List of ideals of QQ[x,y,z] (grevlex) : < x > < xˆ2, y > > dimension(I) [1] 2 > ring("x", "y", "z", coefring = "QQ", code = TRUE) m2rintring00000002 = QQ[x,y,z,MonomialOrder=>{GRevLex=>3}] > Christopher O’Neill (UC Davis) The m2r package August 3, 2017 12 / 20

  35. Convenience functions > (I <- ideal("xˆ2", "x*y", "xˆ3*yˆ2")) M2 Ideal of ring QQ[x,y,z] (grevlex) with generators : < xˆ2, x y, xˆ3 yˆ2 > > primary_decomposition(I) M2 List of ideals of QQ[x,y,z] (grevlex) : < x > < xˆ2, y > > dimension(I) [1] 2 > ring("x", "y", "z", coefring = "QQ", code = TRUE) m2rintring00000002 = QQ[x,y,z,MonomialOrder=>{GRevLex=>3}] > dimension(I, code = TRUE) dim(m2rintideal00000001) Christopher O’Neill (UC Davis) The m2r package August 3, 2017 12 / 20

  36. The parser > Christopher O’Neill (UC Davis) The m2r package August 3, 2017 13 / 20

  37. The parser > m2_matrix(matrix(c(1,2,3,4), nrow = 2, ncol = 2)) [,1] [,2] [1,] 1 3 [2,] 2 4 M2 Matrix over ZZ[] > Christopher O’Neill (UC Davis) The m2r package August 3, 2017 13 / 20

  38. The parser > m2_matrix(matrix(c(1,2,3,4), nrow = 2, ncol = 2)) [,1] [,2] [1,] 1 3 [2,] 2 4 M2 Matrix over ZZ[] > m2_matrix(matrix(c(1,2,3,4), nrow = 2, ncol = 2), code = TRUE) m2rintmatrix00000002 = matrix {{(1),(3)},{(2),(4)}} > Christopher O’Neill (UC Davis) The m2r package August 3, 2017 13 / 20

  39. The parser > m2_matrix(matrix(c(1,2,3,4), nrow = 2, ncol = 2)) [,1] [,2] [1,] 1 3 [2,] 2 4 M2 Matrix over ZZ[] > m2_matrix(matrix(c(1,2,3,4), nrow = 2, ncol = 2), code = TRUE) m2rintmatrix00000002 = matrix {{(1),(3)},{(2),(4)}} > m2("m2rintmatrix00000002 = matrix {{(1),(3)},{(2),(4)}}") [1] "map((ZZ)ˆ2,(ZZ)ˆ2,{{1, 3}, {2, 4}})" > Christopher O’Neill (UC Davis) The m2r package August 3, 2017 13 / 20

  40. The parser > m2_matrix(matrix(c(1,2,3,4), nrow = 2, ncol = 2)) [,1] [,2] [1,] 1 3 [2,] 2 4 M2 Matrix over ZZ[] > m2_matrix(matrix(c(1,2,3,4), nrow = 2, ncol = 2), code = TRUE) m2rintmatrix00000002 = matrix {{(1),(3)},{(2),(4)}} > m2("m2rintmatrix00000002 = matrix {{(1),(3)},{(2),(4)}}") [1] "map((ZZ)ˆ2,(ZZ)ˆ2,{{1, 3}, {2, 4}})" > m2_parse("map((ZZ)ˆ2,(ZZ)ˆ2,{{1, 3}, {2, 4}})") [,1] [,2] [1,] 1 3 [2,] 2 4 M2 Matrix over ZZ[] Christopher O’Neill (UC Davis) The m2r package August 3, 2017 13 / 20

  41. The parser Parsing "map((ZZ)ˆ2,(ZZ)ˆ2,{{1, 3}, {2, 4}})" Christopher O’Neill (UC Davis) The m2r package August 3, 2017 14 / 20

  42. The parser Parsing "map((ZZ)ˆ2,(ZZ)ˆ2,{{1, 3}, {2, 4}})" > m2_tokenize("map((ZZ)ˆ2,(ZZ)ˆ2,{{1, 3}, {2, 4}})") [1] "map" "(" "(" "ZZ" ")" "ˆ" "2" "," "(" "ZZ" [11] ")" "ˆ" "2" "," "{" "{" "1" "," "3" "}" [21] "," "{" "2" "," "4" "}" "}" ")" Christopher O’Neill (UC Davis) The m2r package August 3, 2017 14 / 20

  43. The parser Parsing "map((ZZ)ˆ2,(ZZ)ˆ2,{{1, 3}, {2, 4}})" > m2_tokenize("map((ZZ)ˆ2,(ZZ)ˆ2,{{1, 3}, {2, 4}})") [1] "map" "(" "(" "ZZ" ")" "ˆ" "2" "," "(" "ZZ" [11] ")" "ˆ" "2" "," "{" "{" "1" "," "3" "}" [21] "," "{" "2" "," "4" "}" "}" ")" Christopher O’Neill (UC Davis) The m2r package August 3, 2017 14 / 20

  44. The parser Parsing "map((ZZ)ˆ2,(ZZ)ˆ2,{{1, 3}, {2, 4}})" > m2_tokenize("map((ZZ)ˆ2,(ZZ)ˆ2,{{1, 3}, {2, 4}})") [1] "map" "(" "(" "ZZ" ")" "ˆ" "2" "," "(" "ZZ" [11] ")" "ˆ" "2" "," "{" "{" "1" "," "3" "}" [21] "," "{" "2" "," "4" "}" "}" ")" Christopher O’Neill (UC Davis) The m2r package August 3, 2017 14 / 20

  45. The parser Parsing "map((ZZ)ˆ2,(ZZ)ˆ2,{{1, 3}, {2, 4}})" > m2_tokenize("map((ZZ)ˆ2,(ZZ)ˆ2,{{1, 3}, {2, 4}})") [1] "map" "(" "(" "ZZ" ")" "ˆ" "2" "," "(" "ZZ" [11] ")" "ˆ" "2" "," "{" "{" "1" "," "3" "}" [21] "," "{" "2" "," "4" "}" "}" ")" Christopher O’Neill (UC Davis) The m2r package August 3, 2017 14 / 20

  46. The parser Parsing "map((ZZ)ˆ2,(ZZ)ˆ2,{{1, 3}, {2, 4}})" > m2_tokenize("map((ZZ)ˆ2,(ZZ)ˆ2,{{1, 3}, {2, 4}})") [1] "map" "(" "(" "ZZ" ")" "ˆ" "2" "," "(" "ZZ" [11] ")" "ˆ" "2" "," "{" "{" "1" "," "3" "}" [21] "," "{" "2" "," "4" "}" "}" ")" Christopher O’Neill (UC Davis) The m2r package August 3, 2017 14 / 20

  47. The parser Parsing "map((ZZ)ˆ2,(ZZ)ˆ2,{{1, 3}, {2, 4}})" > m2_tokenize("map((ZZ)ˆ2,(ZZ)ˆ2,{{1, 3}, {2, 4}})") [1] "map" "(" "(" "ZZ" ")" "ˆ" "2" "," "(" "ZZ" [11] ")" "ˆ" "2" "," "{" "{" "1" "," "3" "}" [21] "," "{" "2" "," "4" "}" "}" ")" Christopher O’Neill (UC Davis) The m2r package August 3, 2017 14 / 20

  48. The parser Parsing "map((ZZ)ˆ2,(ZZ)ˆ2,{{1, 3}, {2, 4}})" > m2_tokenize("map((ZZ)ˆ2,(ZZ)ˆ2,{{1, 3}, {2, 4}})") [1] "map" "(" "(" "ZZ" ")" "ˆ" "2" "," "(" "ZZ" [11] ")" "ˆ" "2" "," "{" "{" "1" "," "3" "}" [21] "," "{" "2" "," "4" "}" "}" ")" Christopher O’Neill (UC Davis) The m2r package August 3, 2017 14 / 20

  49. The parser Parsing "map((ZZ)ˆ2,(ZZ)ˆ2,{{1, 3}, {2, 4}})" > m2_tokenize("map((ZZ)ˆ2,(ZZ)ˆ2,{{1, 3}, {2, 4}})") [1] "map" "(" "(" "ZZ" ")" "ˆ" "2" "," "(" "ZZ" [11] ")" "ˆ" "2" "," "{" "{" "1" "," "3" "}" [21] "," "{" "2" "," "4" "}" "}" ")" Christopher O’Neill (UC Davis) The m2r package August 3, 2017 14 / 20

  50. The parser > Christopher O’Neill (UC Davis) The m2r package August 3, 2017 15 / 20

  51. The parser > m2_parse(m2("x")) M2 Symbol: x > Christopher O’Neill (UC Davis) The m2r package August 3, 2017 15 / 20

  52. The parser > m2_parse(m2("x")) M2 Symbol: x > m2_parse(m2("ZZ")) M2 Ring: ZZ[], grevlex order > Christopher O’Neill (UC Davis) The m2r package August 3, 2017 15 / 20

  53. The parser > m2_parse(m2("x")) M2 Symbol: x > m2_parse(m2("ZZ")) M2 Ring: ZZ[], grevlex order > m2("m2rintring00000002 = QQ[x,y,z,MonomialOrder=>{GRevLex=>3}]") [1] "QQ(monoid[x..z, Degrees => {3:1}, Heft => {1}, MonomialOrder => VerticalList{MonomialSize => 32, GRevLex => {3:1}, Position => Up}, DegreeRank => 1])" > Christopher O’Neill (UC Davis) The m2r package August 3, 2017 15 / 20

  54. The parser > m2_parse(m2("x")) M2 Symbol: x > m2_parse(m2("ZZ")) M2 Ring: ZZ[], grevlex order > m2("m2rintring00000002 = QQ[x,y,z,MonomialOrder=>{GRevLex=>3}]") [1] "QQ(monoid[x..z, Degrees => {3:1}, Heft => {1}, MonomialOrder => VerticalList{MonomialSize => 32, GRevLex => {3:1}, Position => Up}, DegreeRank => 1])" > m2_parse(m2("m2rintring00000002")) M2 Ring: QQ[x,y,z], grevlex order > Christopher O’Neill (UC Davis) The m2r package August 3, 2017 15 / 20

  55. The parser > m2_parse(m2("x")) M2 Symbol: x > m2_parse(m2("ZZ")) M2 Ring: ZZ[], grevlex order > m2("m2rintring00000002 = QQ[x,y,z,MonomialOrder=>{GRevLex=>3}]") [1] "QQ(monoid[x..z, Degrees => {3:1}, Heft => {1}, MonomialOrder => VerticalList{MonomialSize => 32, GRevLex => {3:1}, Position => Up}, DegreeRank => 1])" > m2_parse(m2("m2rintring00000002")) M2 Ring: QQ[x,y,z], grevlex order > m2("ideal({xˆ2+2*x,2*x+3})") [1] "ideal map((m2rintring00000002)ˆ1,(m2rintring00000002)ˆ{{-2}, {-1}},{{xˆ2+2*x, 2*x+3}})" Christopher O’Neill (UC Davis) The m2r package August 3, 2017 15 / 20

  56. Parser “extensibility” > m2("ideal({xˆ2+2*x,2*x+3})") [1] "ideal map((m2rintring00000002)ˆ1,(m2rintring00000002)ˆ{{-2}, {-1}},{{xˆ2+2*x, 2*x+3}})" Christopher O’Neill (UC Davis) The m2r package August 3, 2017 16 / 20

  57. Parser “extensibility” > m2("ideal({xˆ2+2*x,2*x+3})") [1] "ideal map((m2rintring00000002)ˆ1,(m2rintring00000002)ˆ{{-2}, {-1}},{{xˆ2+2*x, 2*x+3}})" m2_parse_function.m2_map <- function(x) { R1 <- x[[1]] R2 <- x[[2]] . . . m2_structure( mat, m2_name = "", m2_class = "m2_matrix", m2_meta = list( ring = R1 ), base_class = "matrix" ) } Christopher O’Neill (UC Davis) The m2r package August 3, 2017 16 / 20

  58. Parser “extensibility” > m2("ideal({xˆ2+2*x,2*x+3})") [1] "ideal map((m2rintring00000002)ˆ1,(m2rintring00000002)ˆ{{-2}, {-1}},{{xˆ2+2*x, 2*x+3}})" Christopher O’Neill (UC Davis) The m2r package August 3, 2017 16 / 20

  59. Parser “extensibility” > m2("ideal({xˆ2+2*x,2*x+3})") [1] "ideal map((m2rintring00000002)ˆ1,(m2rintring00000002)ˆ{{-2}, {-1}},{{xˆ2+2*x, 2*x+3}})" m2_parse_function.m2_ideal <- function(x) { m2_structure( m2_name = "", m2_class = "m2_ideal", m2_meta = list( ring = m2_meta(x[[1]], "ring"), gens = structure(x[[1]][1,], class = "mpolyList") ) ) } Christopher O’Neill (UC Davis) The m2r package August 3, 2017 16 / 20

  60. m2r is now in the cloud! > Christopher O’Neill (UC Davis) The m2r package August 3, 2017 17 / 20

  61. m2r is now in the cloud! > library("m2r") Loading required package: mpoly Loading required package: stringr please cite mpoly if you use it; see citation("mpoly") M2 not found; defaulting to cloud. Use set_m2r_path("/path/to/m2") to run M2 locally. > Christopher O’Neill (UC Davis) The m2r package August 3, 2017 17 / 20

  62. m2r is now in the cloud! > library("m2r") Loading required package: mpoly Loading required package: stringr please cite mpoly if you use it; see citation("mpoly") M2 not found; defaulting to cloud. Use set_m2r_path("/path/to/m2") to run M2 locally. > start_m2() Connecting to M2 in the cloud... done. > Christopher O’Neill (UC Davis) The m2r package August 3, 2017 17 / 20

  63. m2r is now in the cloud! > library("m2r") Loading required package: mpoly Loading required package: stringr please cite mpoly if you use it; see citation("mpoly") M2 not found; defaulting to cloud. Use set_m2r_path("/path/to/m2") to run M2 locally. > start_m2() Connecting to M2 in the cloud... done. > m2("a = 5") [1] "5" > Christopher O’Neill (UC Davis) The m2r package August 3, 2017 17 / 20

  64. m2r is now in the cloud! > library("m2r") Loading required package: mpoly Loading required package: stringr please cite mpoly if you use it; see citation("mpoly") M2 not found; defaulting to cloud. Use set_m2r_path("/path/to/m2") to run M2 locally. > start_m2() Connecting to M2 in the cloud... done. > m2("a = 5") [1] "5" > m2("a") [1] "5" Christopher O’Neill (UC Davis) The m2r package August 3, 2017 17 / 20

  65. m2r is now in the cloud! > library("m2r") Loading required package: mpoly Loading required package: stringr please cite mpoly if you use it; see citation("mpoly") M2 not found; defaulting to cloud. Use set_m2r_path("/path/to/m2") to run M2 locally. > start_m2() Connecting to M2 in the cloud... done. > m2("a = 5") [1] "5" > m2("a") [1] "5" Christopher O’Neill (UC Davis) The m2r package August 3, 2017 17 / 20

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