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Expression of type ExprTuple

from the theory of proveit.linear_algebra.tensors

In [1]:
import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import ExprTuple, alpha, fi, i, x, y, z
from proveit.linear_algebra import ScalarMult, TensorProd, VecSum
from proveit.numbers import Interval, four, two
In [2]:
# build up the expression from sub-expressions
sub_expr1 = [i]
sub_expr2 = Interval(two, four)
expr = ExprTuple(ScalarMult(alpha, VecSum(index_or_indices = sub_expr1, summand = TensorProd(x, y, fi, z), domain = sub_expr2)), ScalarMult(alpha, TensorProd(x, y, VecSum(index_or_indices = sub_expr1, summand = fi, domain = sub_expr2), z)))
expr:
In [3]:
# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")
Passed sanity check: expr matches stored_expr
In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
\left(\alpha \cdot \left(\sum_{i=2}^{4} \left(x {\otimes} y {\otimes} f\left(i\right) {\otimes} z\right)\right), \alpha \cdot \left(x {\otimes} y {\otimes} \left(\sum_{i=2}^{4} f\left(i\right)\right) {\otimes} z\right)\right)
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
wrap_positionsposition(s) at which wrapping is to occur; 'n' is after the nth comma.()()('with_wrapping_at',)
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'leftleft('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0ExprTuple1, 2
1Operationoperator: 4
operands: 3
2Operationoperator: 4
operands: 5
3ExprTuple7, 6
4Literal
5ExprTuple7, 8
6Operationoperator: 14
operand: 11
7Variable
8Operationoperator: 18
operands: 10
9ExprTuple11
10ExprTuple21, 22, 12, 23
11Lambdaparameter: 30
body: 13
12Operationoperator: 14
operand: 17
13Conditionalvalue: 16
condition: 25
14Literal
15ExprTuple17
16Operationoperator: 18
operands: 19
17Lambdaparameter: 30
body: 20
18Literal
19ExprTuple21, 22, 24, 23
20Conditionalvalue: 24
condition: 25
21Variable
22Variable
23Variable
24Operationoperator: 26
operand: 30
25Operationoperator: 28
operands: 29
26Variable
27ExprTuple30
28Literal
29ExprTuple30, 31
30Variable
31Operationoperator: 32
operands: 33
32Literal
33ExprTuple34, 35
34Literal
35Literal