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Expression of type Mult

from the theory of proveit.numbers.multiplication

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 a, b, k, theta
from proveit.numbers import Add, Exp, Mult, e, i, pi, two
In [2]:
# build up the expression from sub-expressions
expr = Mult(Exp(a, k), Exp(Mult(Exp(e, Mult(two, pi, i, theta)), Add(a, b)), k), Exp(e, Mult(two, pi, i, b)))
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())
a^{k} \cdot \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \theta} \cdot \left(a + b\right)\right)^{k} \cdot \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot b}
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
operation'infix' or 'function' style formattinginfixinfix
wrap_positionsposition(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.()()('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'centercenter('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 23
operands: 1
1ExprTuple2, 3, 4
2Operationoperator: 15
operands: 5
3Operationoperator: 15
operands: 6
4Operationoperator: 15
operands: 7
5ExprTuple21, 9
6ExprTuple8, 9
7ExprTuple19, 10
8Operationoperator: 23
operands: 11
9Variable
10Operationoperator: 23
operands: 12
11ExprTuple13, 14
12ExprTuple25, 26, 27, 22
13Operationoperator: 15
operands: 16
14Operationoperator: 17
operands: 18
15Literal
16ExprTuple19, 20
17Literal
18ExprTuple21, 22
19Literal
20Operationoperator: 23
operands: 24
21Variable
22Variable
23Literal
24ExprTuple25, 26, 27, 28
25Literal
26Literal
27Literal
28Variable